internlm/Lean-Github · Datasets at Hugging Face

url stringclasses 147 values	commit stringclasses 147 values	file_path stringlengths 7 101	full_name stringlengths 1 94	start stringlengths 6 10	end stringlengths 6 11	tactic stringlengths 1 11.2k	state_before stringlengths 3 2.09M	state_after stringlengths 6 2.09M
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.GCL.BigStep_choice	[147, 9]	[164, 23]	cases hex with \| intro hless hstep => apply BigStep.choice <;> assumption	case mpr.intro Ss : List Stmt s t : State i : ℕ hex : ∃ hless, (Ss[i], s) ⟹ t ⊢ (Stmt.choice Ss, s) ⟹ t	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.GCL.BigStep_choice	[147, 9]	[164, 23]	apply BigStep.choice <;> assumption	case mpr.intro.intro Ss : List Stmt s t : State i : ℕ hless : i < List.length Ss hstep : (Ss[i], s) ⟹ t ⊢ (Stmt.choice Ss, s) ⟹ t	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.refl	[213, 1]	[217, 11]	rfl	S : Stmt s t : State ⊢ (S, s) ⟹ t ↔ (S, s) ⟹ t	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.skip_assign_id	[234, 1]	[244, 17]	intro s t	x : String ⊢ (Stmt.assign x fun s => s x) ~ Stmt.skip	x : String s t : State ⊢ (Stmt.assign x fun s => s x, s) ⟹ t ↔ (Stmt.skip, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.skip_assign_id	[234, 1]	[244, 17]	apply Iff.intro	x : String s t : State ⊢ (Stmt.assign x fun s => s x, s) ⟹ t ↔ (Stmt.skip, s) ⟹ t	case mp x : String s t : State ⊢ (Stmt.assign x fun s => s x, s) ⟹ t → (Stmt.skip, s) ⟹ t case mpr x : String s t : State ⊢ (Stmt.skip, s) ⟹ t → (Stmt.assign x fun s => s x, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.skip_assign_id	[234, 1]	[244, 17]	{ intro hasn cases hasn simp [*] }	case mp x : String s t : State ⊢ (Stmt.assign x fun s => s x, s) ⟹ t → (Stmt.skip, s) ⟹ t case mpr x : String s t : State ⊢ (Stmt.skip, s) ⟹ t → (Stmt.assign x fun s => s x, s) ⟹ t	case mpr x : String s t : State ⊢ (Stmt.skip, s) ⟹ t → (Stmt.assign x fun s => s x, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.skip_assign_id	[234, 1]	[244, 17]	{ intro hskip cases hskip simp [*] }	case mpr x : String s t : State ⊢ (Stmt.skip, s) ⟹ t → (Stmt.assign x fun s => s x, s) ⟹ t	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.skip_assign_id	[234, 1]	[244, 17]	intro hasn	case mp x : String s t : State ⊢ (Stmt.assign x fun s => s x, s) ⟹ t → (Stmt.skip, s) ⟹ t	case mp x : String s t : State hasn : (Stmt.assign x fun s => s x, s) ⟹ t ⊢ (Stmt.skip, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.skip_assign_id	[234, 1]	[244, 17]	cases hasn	case mp x : String s t : State hasn : (Stmt.assign x fun s => s x, s) ⟹ t ⊢ (Stmt.skip, s) ⟹ t	case mp.assign x : String s : State ⊢ (Stmt.skip, s) ⟹ State.update x ((fun s => s x) s) s
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.skip_assign_id	[234, 1]	[244, 17]	simp [*]	case mp.assign x : String s : State ⊢ (Stmt.skip, s) ⟹ State.update x ((fun s => s x) s) s	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.skip_assign_id	[234, 1]	[244, 17]	intro hskip	case mpr x : String s t : State ⊢ (Stmt.skip, s) ⟹ t → (Stmt.assign x fun s => s x, s) ⟹ t	case mpr x : String s t : State hskip : (Stmt.skip, s) ⟹ t ⊢ (Stmt.assign x fun s => s x, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.skip_assign_id	[234, 1]	[244, 17]	cases hskip	case mpr x : String s t : State hskip : (Stmt.skip, s) ⟹ t ⊢ (Stmt.assign x fun s => s x, s) ⟹ t	case mpr.skip x : String s : State ⊢ (Stmt.assign x fun s => s x, s) ⟹ s
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.skip_assign_id	[234, 1]	[244, 17]	simp [*]	case mpr.skip x : String s : State ⊢ (Stmt.assign x fun s => s x, s) ⟹ s	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_skip_left	[246, 1]	[259, 23]	intro s t	S : Stmt ⊢ Stmt.skip; S ~ S	S : Stmt s t : State ⊢ (Stmt.skip; S, s) ⟹ t ↔ (S, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_skip_left	[246, 1]	[259, 23]	apply Iff.intro	S : Stmt s t : State ⊢ (Stmt.skip; S, s) ⟹ t ↔ (S, s) ⟹ t	case mp S : Stmt s t : State ⊢ (Stmt.skip; S, s) ⟹ t → (S, s) ⟹ t case mpr S : Stmt s t : State ⊢ (S, s) ⟹ t → (Stmt.skip; S, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_skip_left	[246, 1]	[259, 23]	{ intro hseq cases hseq with \| seq _ _ _ u _ hs hS => cases hs assumption }	case mp S : Stmt s t : State ⊢ (Stmt.skip; S, s) ⟹ t → (S, s) ⟹ t case mpr S : Stmt s t : State ⊢ (S, s) ⟹ t → (Stmt.skip; S, s) ⟹ t	case mpr S : Stmt s t : State ⊢ (S, s) ⟹ t → (Stmt.skip; S, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_skip_left	[246, 1]	[259, 23]	{ intro hS apply BigStep.seq { apply BigStep.skip } { assumption } }	case mpr S : Stmt s t : State ⊢ (S, s) ⟹ t → (Stmt.skip; S, s) ⟹ t	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_skip_left	[246, 1]	[259, 23]	intro hseq	case mp S : Stmt s t : State ⊢ (Stmt.skip; S, s) ⟹ t → (S, s) ⟹ t	case mp S : Stmt s t : State hseq : (Stmt.skip; S, s) ⟹ t ⊢ (S, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_skip_left	[246, 1]	[259, 23]	cases hseq with \| seq _ _ _ u _ hs hS => cases hs assumption	case mp S : Stmt s t : State hseq : (Stmt.skip; S, s) ⟹ t ⊢ (S, s) ⟹ t	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_skip_left	[246, 1]	[259, 23]	cases hs	case mp.seq S : Stmt s t u : State hs : (Stmt.skip, s) ⟹ u hS : (S, u) ⟹ t ⊢ (S, s) ⟹ t	case mp.seq.skip S : Stmt s t : State hS : (S, s) ⟹ t ⊢ (S, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_skip_left	[246, 1]	[259, 23]	assumption	case mp.seq.skip S : Stmt s t : State hS : (S, s) ⟹ t ⊢ (S, s) ⟹ t	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_skip_left	[246, 1]	[259, 23]	intro hS	case mpr S : Stmt s t : State ⊢ (S, s) ⟹ t → (Stmt.skip; S, s) ⟹ t	case mpr S : Stmt s t : State hS : (S, s) ⟹ t ⊢ (Stmt.skip; S, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_skip_left	[246, 1]	[259, 23]	apply BigStep.seq	case mpr S : Stmt s t : State hS : (S, s) ⟹ t ⊢ (Stmt.skip; S, s) ⟹ t	case mpr.hS S : Stmt s t : State hS : (S, s) ⟹ t ⊢ (Stmt.skip, s) ⟹ ?mpr.t case mpr.hT S : Stmt s t : State hS : (S, s) ⟹ t ⊢ (S, ?mpr.t) ⟹ t case mpr.t S : Stmt s t : State hS : (S, s) ⟹ t ⊢ State
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_skip_left	[246, 1]	[259, 23]	{ apply BigStep.skip }	case mpr.hS S : Stmt s t : State hS : (S, s) ⟹ t ⊢ (Stmt.skip, s) ⟹ ?mpr.t case mpr.hT S : Stmt s t : State hS : (S, s) ⟹ t ⊢ (S, ?mpr.t) ⟹ t case mpr.t S : Stmt s t : State hS : (S, s) ⟹ t ⊢ State	case mpr.hT S : Stmt s t : State hS : (S, s) ⟹ t ⊢ (S, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_skip_left	[246, 1]	[259, 23]	{ assumption }	case mpr.hT S : Stmt s t : State hS : (S, s) ⟹ t ⊢ (S, s) ⟹ t	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_skip_left	[246, 1]	[259, 23]	apply BigStep.skip	case mpr.hS S : Stmt s t : State hS : (S, s) ⟹ t ⊢ (Stmt.skip, s) ⟹ ?mpr.t	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_skip_left	[246, 1]	[259, 23]	assumption	case mpr.hT S : Stmt s t : State hS : (S, s) ⟹ t ⊢ (S, s) ⟹ t	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_skip_right	[261, 1]	[274, 31]	intro s t	S : Stmt ⊢ S; Stmt.skip ~ S	S : Stmt s t : State ⊢ (S; Stmt.skip, s) ⟹ t ↔ (S, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_skip_right	[261, 1]	[274, 31]	apply Iff.intro	S : Stmt s t : State ⊢ (S; Stmt.skip, s) ⟹ t ↔ (S, s) ⟹ t	case mp S : Stmt s t : State ⊢ (S; Stmt.skip, s) ⟹ t → (S, s) ⟹ t case mpr S : Stmt s t : State ⊢ (S, s) ⟹ t → (S; Stmt.skip, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_skip_right	[261, 1]	[274, 31]	{ intro hseq cases hseq with \| seq _ _ _ u _ hS hs => cases hs assumption }	case mp S : Stmt s t : State ⊢ (S; Stmt.skip, s) ⟹ t → (S, s) ⟹ t case mpr S : Stmt s t : State ⊢ (S, s) ⟹ t → (S; Stmt.skip, s) ⟹ t	case mpr S : Stmt s t : State ⊢ (S, s) ⟹ t → (S; Stmt.skip, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_skip_right	[261, 1]	[274, 31]	{ intro h apply BigStep.seq { assumption } { apply BigStep.skip } }	case mpr S : Stmt s t : State ⊢ (S, s) ⟹ t → (S; Stmt.skip, s) ⟹ t	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_skip_right	[261, 1]	[274, 31]	intro hseq	case mp S : Stmt s t : State ⊢ (S; Stmt.skip, s) ⟹ t → (S, s) ⟹ t	case mp S : Stmt s t : State hseq : (S; Stmt.skip, s) ⟹ t ⊢ (S, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_skip_right	[261, 1]	[274, 31]	cases hseq with \| seq _ _ _ u _ hS hs => cases hs assumption	case mp S : Stmt s t : State hseq : (S; Stmt.skip, s) ⟹ t ⊢ (S, s) ⟹ t	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_skip_right	[261, 1]	[274, 31]	cases hs	case mp.seq S : Stmt s t u : State hS : (S, s) ⟹ u hs : (Stmt.skip, u) ⟹ t ⊢ (S, s) ⟹ t	case mp.seq.skip S : Stmt s t : State hS : (S, s) ⟹ t ⊢ (S, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_skip_right	[261, 1]	[274, 31]	assumption	case mp.seq.skip S : Stmt s t : State hS : (S, s) ⟹ t ⊢ (S, s) ⟹ t	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_skip_right	[261, 1]	[274, 31]	intro h	case mpr S : Stmt s t : State ⊢ (S, s) ⟹ t → (S; Stmt.skip, s) ⟹ t	case mpr S : Stmt s t : State h : (S, s) ⟹ t ⊢ (S; Stmt.skip, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_skip_right	[261, 1]	[274, 31]	apply BigStep.seq	case mpr S : Stmt s t : State h : (S, s) ⟹ t ⊢ (S; Stmt.skip, s) ⟹ t	case mpr.hS S : Stmt s t : State h : (S, s) ⟹ t ⊢ (S, s) ⟹ ?mpr.t case mpr.hT S : Stmt s t : State h : (S, s) ⟹ t ⊢ (Stmt.skip, ?mpr.t) ⟹ t case mpr.t S : Stmt s t : State h : (S, s) ⟹ t ⊢ State
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_skip_right	[261, 1]	[274, 31]	{ assumption }	case mpr.hS S : Stmt s t : State h : (S, s) ⟹ t ⊢ (S, s) ⟹ ?mpr.t case mpr.hT S : Stmt s t : State h : (S, s) ⟹ t ⊢ (Stmt.skip, ?mpr.t) ⟹ t case mpr.t S : Stmt s t : State h : (S, s) ⟹ t ⊢ State	case mpr.hT S : Stmt s t : State h : (S, s) ⟹ t ⊢ (Stmt.skip, t) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_skip_right	[261, 1]	[274, 31]	{ apply BigStep.skip }	case mpr.hT S : Stmt s t : State h : (S, s) ⟹ t ⊢ (Stmt.skip, t) ⟹ t	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_skip_right	[261, 1]	[274, 31]	assumption	case mpr.hS S : Stmt s t : State h : (S, s) ⟹ t ⊢ (S, s) ⟹ ?mpr.t	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_skip_right	[261, 1]	[274, 31]	apply BigStep.skip	case mpr.hT S : Stmt s t : State h : (S, s) ⟹ t ⊢ (Stmt.skip, t) ⟹ t	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.if_seq_while_skip	[276, 1]	[302, 29]	intro s t	B : State → Prop S : Stmt ⊢ Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip ~ Stmt.whileDo B S	B : State → Prop S : Stmt s t : State ⊢ (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⟹ t ↔ (Stmt.whileDo B S, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.if_seq_while_skip	[276, 1]	[302, 29]	apply Iff.intro	B : State → Prop S : Stmt s t : State ⊢ (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⟹ t ↔ (Stmt.whileDo B S, s) ⟹ t	case mp B : State → Prop S : Stmt s t : State ⊢ (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⟹ t → (Stmt.whileDo B S, s) ⟹ t case mpr B : State → Prop S : Stmt s t : State ⊢ (Stmt.whileDo B S, s) ⟹ t → (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.if_seq_while_skip	[276, 1]	[302, 29]	{ intro hif cases hif with \| if_true _ _ _ _ _ hB hseq => cases hseq with \| seq _ _ _ u _ hS hT => apply BigStep.while_true <;> assumption \| if_false _ _ _ _ _ hB hskip => cases hskip apply BigStep.while_false assumption }	case mp B : State → Prop S : Stmt s t : State ⊢ (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⟹ t → (Stmt.whileDo B S, s) ⟹ t case mpr B : State → Prop S : Stmt s t : State ⊢ (Stmt.whileDo B S, s) ⟹ t → (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⟹ t	case mpr B : State → Prop S : Stmt s t : State ⊢ (Stmt.whileDo B S, s) ⟹ t → (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.if_seq_while_skip	[276, 1]	[302, 29]	{ intro hwhile cases hwhile with \| while_true _ _ _ u _ hB hS hw => apply BigStep.if_true exact hB apply BigStep.seq <;> assumption \| while_false _ _ _ hB => apply BigStep.if_false exact hB apply BigStep.skip }	case mpr B : State → Prop S : Stmt s t : State ⊢ (Stmt.whileDo B S, s) ⟹ t → (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⟹ t	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.if_seq_while_skip	[276, 1]	[302, 29]	intro hif	case mp B : State → Prop S : Stmt s t : State ⊢ (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⟹ t → (Stmt.whileDo B S, s) ⟹ t	case mp B : State → Prop S : Stmt s t : State hif : (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⟹ t ⊢ (Stmt.whileDo B S, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.if_seq_while_skip	[276, 1]	[302, 29]	cases hif with \| if_true _ _ _ _ _ hB hseq => cases hseq with \| seq _ _ _ u _ hS hT => apply BigStep.while_true <;> assumption \| if_false _ _ _ _ _ hB hskip => cases hskip apply BigStep.while_false assumption	case mp B : State → Prop S : Stmt s t : State hif : (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⟹ t ⊢ (Stmt.whileDo B S, s) ⟹ t	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.if_seq_while_skip	[276, 1]	[302, 29]	cases hseq with \| seq _ _ _ u _ hS hT => apply BigStep.while_true <;> assumption	case mp.if_true B : State → Prop S : Stmt s t : State hB : B s hseq : (S; Stmt.whileDo B S, s) ⟹ t ⊢ (Stmt.whileDo B S, s) ⟹ t	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.if_seq_while_skip	[276, 1]	[302, 29]	apply BigStep.while_true <;> assumption	case mp.if_true.seq B : State → Prop S : Stmt s t : State hB : B s u : State hS : (S, s) ⟹ u hT : (Stmt.whileDo B S, u) ⟹ t ⊢ (Stmt.whileDo B S, s) ⟹ t	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.if_seq_while_skip	[276, 1]	[302, 29]	cases hskip	case mp.if_false B : State → Prop S : Stmt s t : State hB : ¬B s hskip : (Stmt.skip, s) ⟹ t ⊢ (Stmt.whileDo B S, s) ⟹ t	case mp.if_false.skip B : State → Prop S : Stmt s : State hB : ¬B s ⊢ (Stmt.whileDo B S, s) ⟹ s
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.if_seq_while_skip	[276, 1]	[302, 29]	apply BigStep.while_false	case mp.if_false.skip B : State → Prop S : Stmt s : State hB : ¬B s ⊢ (Stmt.whileDo B S, s) ⟹ s	case mp.if_false.skip.hcond B : State → Prop S : Stmt s : State hB : ¬B s ⊢ ¬B s
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.if_seq_while_skip	[276, 1]	[302, 29]	assumption	case mp.if_false.skip.hcond B : State → Prop S : Stmt s : State hB : ¬B s ⊢ ¬B s	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.if_seq_while_skip	[276, 1]	[302, 29]	intro hwhile	case mpr B : State → Prop S : Stmt s t : State ⊢ (Stmt.whileDo B S, s) ⟹ t → (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⟹ t	case mpr B : State → Prop S : Stmt s t : State hwhile : (Stmt.whileDo B S, s) ⟹ t ⊢ (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.if_seq_while_skip	[276, 1]	[302, 29]	cases hwhile with \| while_true _ _ _ u _ hB hS hw => apply BigStep.if_true exact hB apply BigStep.seq <;> assumption \| while_false _ _ _ hB => apply BigStep.if_false exact hB apply BigStep.skip	case mpr B : State → Prop S : Stmt s t : State hwhile : (Stmt.whileDo B S, s) ⟹ t ⊢ (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⟹ t	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.if_seq_while_skip	[276, 1]	[302, 29]	apply BigStep.if_true	case mpr.while_true B : State → Prop S : Stmt s t u : State hB : B s hS : (S, s) ⟹ u hw : (Stmt.whileDo B S, u) ⟹ t ⊢ (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⟹ t	case mpr.while_true.hcond B : State → Prop S : Stmt s t u : State hB : B s hS : (S, s) ⟹ u hw : (Stmt.whileDo B S, u) ⟹ t ⊢ B s case mpr.while_true.hbody B : State → Prop S : Stmt s t u : State hB : B s hS : (S, s) ⟹ u hw : (Stmt.whileDo B S, u) ⟹ t ⊢ (S; Stmt.whileDo B S, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.if_seq_while_skip	[276, 1]	[302, 29]	exact hB	case mpr.while_true.hcond B : State → Prop S : Stmt s t u : State hB : B s hS : (S, s) ⟹ u hw : (Stmt.whileDo B S, u) ⟹ t ⊢ B s case mpr.while_true.hbody B : State → Prop S : Stmt s t u : State hB : B s hS : (S, s) ⟹ u hw : (Stmt.whileDo B S, u) ⟹ t ⊢ (S; Stmt.whileDo B S, s) ⟹ t	case mpr.while_true.hbody B : State → Prop S : Stmt s t u : State hB : B s hS : (S, s) ⟹ u hw : (Stmt.whileDo B S, u) ⟹ t ⊢ (S; Stmt.whileDo B S, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.if_seq_while_skip	[276, 1]	[302, 29]	apply BigStep.seq <;> assumption	case mpr.while_true.hbody B : State → Prop S : Stmt s t u : State hB : B s hS : (S, s) ⟹ u hw : (Stmt.whileDo B S, u) ⟹ t ⊢ (S; Stmt.whileDo B S, s) ⟹ t	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.if_seq_while_skip	[276, 1]	[302, 29]	apply BigStep.if_false	case mpr.while_false B : State → Prop S : Stmt s : State hB : ¬B s ⊢ (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⟹ s	case mpr.while_false.hcond B : State → Prop S : Stmt s : State hB : ¬B s ⊢ ¬B s case mpr.while_false.hbody B : State → Prop S : Stmt s : State hB : ¬B s ⊢ (Stmt.skip, s) ⟹ s
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.if_seq_while_skip	[276, 1]	[302, 29]	exact hB	case mpr.while_false.hcond B : State → Prop S : Stmt s : State hB : ¬B s ⊢ ¬B s case mpr.while_false.hbody B : State → Prop S : Stmt s : State hB : ¬B s ⊢ (Stmt.skip, s) ⟹ s	case mpr.while_false.hbody B : State → Prop S : Stmt s : State hB : ¬B s ⊢ (Stmt.skip, s) ⟹ s
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.if_seq_while_skip	[276, 1]	[302, 29]	apply BigStep.skip	case mpr.while_false.hbody B : State → Prop S : Stmt s : State hB : ¬B s ⊢ (Stmt.skip, s) ⟹ s	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_congr	[308, 1]	[333, 25]	intro s t	S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ ⊢ S₁; T₁ ~ S₂; T₂	S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (S₁; T₁, s) ⟹ t ↔ (S₂; T₂, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_congr	[308, 1]	[333, 25]	apply Iff.intro	S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (S₁; T₁, s) ⟹ t ↔ (S₂; T₂, s) ⟹ t	case mp S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (S₁; T₁, s) ⟹ t → (S₂; T₂, s) ⟹ t case mpr S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (S₂; T₂, s) ⟹ t → (S₁; T₁, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_congr	[308, 1]	[333, 25]	{ intro hseq cases hseq with \| seq _ _ _ u _ hS₁ hT₁ => apply BigStep.seq { rw [BigStepEquiv] at hS rw [← hS] assumption } { rw [BigStepEquiv] at hT rw [← hT] assumption } }	case mp S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (S₁; T₁, s) ⟹ t → (S₂; T₂, s) ⟹ t case mpr S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (S₂; T₂, s) ⟹ t → (S₁; T₁, s) ⟹ t	case mpr S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (S₂; T₂, s) ⟹ t → (S₁; T₁, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_congr	[308, 1]	[333, 25]	{ intro hseq cases hseq with \| seq _ _ _ u _ hS₂ hT₂ => apply BigStep.seq { rw [BigStepEquiv] at hS rw [hS] assumption } { rw [BigStepEquiv] at hT rw [hT] assumption } }	case mpr S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (S₂; T₂, s) ⟹ t → (S₁; T₁, s) ⟹ t	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_congr	[308, 1]	[333, 25]	intro hseq	case mp S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (S₁; T₁, s) ⟹ t → (S₂; T₂, s) ⟹ t	case mp S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hseq : (S₁; T₁, s) ⟹ t ⊢ (S₂; T₂, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_congr	[308, 1]	[333, 25]	cases hseq with \| seq _ _ _ u _ hS₁ hT₁ => apply BigStep.seq { rw [BigStepEquiv] at hS rw [← hS] assumption } { rw [BigStepEquiv] at hT rw [← hT] assumption }	case mp S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hseq : (S₁; T₁, s) ⟹ t ⊢ (S₂; T₂, s) ⟹ t	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_congr	[308, 1]	[333, 25]	apply BigStep.seq	case mp.seq S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ (S₂; T₂, s) ⟹ t	case mp.seq.hS S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ (S₂, s) ⟹ ?mp.seq.t case mp.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ (T₂, ?mp.seq.t) ⟹ t case mp.seq.t S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ State
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_congr	[308, 1]	[333, 25]	{ rw [BigStepEquiv] at hS rw [← hS] assumption }	case mp.seq.hS S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ (S₂, s) ⟹ ?mp.seq.t case mp.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ (T₂, ?mp.seq.t) ⟹ t case mp.seq.t S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ State	case mp.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ (T₂, u) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_congr	[308, 1]	[333, 25]	{ rw [BigStepEquiv] at hT rw [← hT] assumption }	case mp.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ (T₂, u) ⟹ t	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_congr	[308, 1]	[333, 25]	rw [BigStepEquiv] at hS	case mp.seq.hS S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ (S₂, s) ⟹ ?mp.seq.t	case mp.seq.hS S₁ S₂ T₁ T₂ : Stmt hS✝ : S₁ ~ S₂ hS : ∀ (s t : State), (S₁, s) ⟹ t ↔ (S₂, s) ⟹ t hT : T₁ ~ T₂ s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ (S₂, s) ⟹ ?m.68459 hT s t u hS₁ hT₁
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_congr	[308, 1]	[333, 25]	rw [← hS]	case mp.seq.hS S₁ S₂ T₁ T₂ : Stmt hS✝ : S₁ ~ S₂ hS : ∀ (s t : State), (S₁, s) ⟹ t ↔ (S₂, s) ⟹ t hT : T₁ ~ T₂ s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ (S₂, s) ⟹ ?m.68459 hT s t u hS₁ hT₁	case mp.seq.hS S₁ S₂ T₁ T₂ : Stmt hS✝ : S₁ ~ S₂ hS : ∀ (s t : State), (S₁, s) ⟹ t ↔ (S₂, s) ⟹ t hT : T₁ ~ T₂ s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ (S₁, s) ⟹ ?m.68459 hT s t u hS₁ hT₁ S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ ⊢ T₁ ~ T₂ → (s t u : State) → (S₁, s) ⟹ u → (T₁, u) ⟹ t → State
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_congr	[308, 1]	[333, 25]	assumption	case mp.seq.hS S₁ S₂ T₁ T₂ : Stmt hS✝ : S₁ ~ S₂ hS : ∀ (s t : State), (S₁, s) ⟹ t ↔ (S₂, s) ⟹ t hT : T₁ ~ T₂ s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ (S₁, s) ⟹ ?m.68459 hT s t u hS₁ hT₁ S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ ⊢ T₁ ~ T₂ → (s t u : State) → (S₁, s) ⟹ u → (T₁, u) ⟹ t → State	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_congr	[308, 1]	[333, 25]	rw [BigStepEquiv] at hT	case mp.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ (T₂, u) ⟹ t	case mp.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : ∀ (s t : State), (T₁, s) ⟹ t ↔ (T₂, s) ⟹ t s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ (T₂, u) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_congr	[308, 1]	[333, 25]	rw [← hT]	case mp.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : ∀ (s t : State), (T₁, s) ⟹ t ↔ (T₂, s) ⟹ t s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ (T₂, u) ⟹ t	case mp.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : ∀ (s t : State), (T₁, s) ⟹ t ↔ (T₂, s) ⟹ t s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ (T₁, u) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_congr	[308, 1]	[333, 25]	assumption	case mp.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : ∀ (s t : State), (T₁, s) ⟹ t ↔ (T₂, s) ⟹ t s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ (T₁, u) ⟹ t	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_congr	[308, 1]	[333, 25]	intro hseq	case mpr S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (S₂; T₂, s) ⟹ t → (S₁; T₁, s) ⟹ t	case mpr S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hseq : (S₂; T₂, s) ⟹ t ⊢ (S₁; T₁, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_congr	[308, 1]	[333, 25]	cases hseq with \| seq _ _ _ u _ hS₂ hT₂ => apply BigStep.seq { rw [BigStepEquiv] at hS rw [hS] assumption } { rw [BigStepEquiv] at hT rw [hT] assumption }	case mpr S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hseq : (S₂; T₂, s) ⟹ t ⊢ (S₁; T₁, s) ⟹ t	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_congr	[308, 1]	[333, 25]	apply BigStep.seq	case mpr.seq S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ (S₁; T₁, s) ⟹ t	case mpr.seq.hS S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ (S₁, s) ⟹ ?mpr.seq.t case mpr.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ (T₁, ?mpr.seq.t) ⟹ t case mpr.seq.t S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ State
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_congr	[308, 1]	[333, 25]	{ rw [BigStepEquiv] at hS rw [hS] assumption }	case mpr.seq.hS S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ (S₁, s) ⟹ ?mpr.seq.t case mpr.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ (T₁, ?mpr.seq.t) ⟹ t case mpr.seq.t S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ State	case mpr.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ (T₁, u) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_congr	[308, 1]	[333, 25]	{ rw [BigStepEquiv] at hT rw [hT] assumption }	case mpr.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ (T₁, u) ⟹ t	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_congr	[308, 1]	[333, 25]	rw [BigStepEquiv] at hS	case mpr.seq.hS S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ (S₁, s) ⟹ ?mpr.seq.t	case mpr.seq.hS S₁ S₂ T₁ T₂ : Stmt hS✝ : S₁ ~ S₂ hS : ∀ (s t : State), (S₁, s) ⟹ t ↔ (S₂, s) ⟹ t hT : T₁ ~ T₂ s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ (S₁, s) ⟹ ?m.68939 hT s t u hS₂ hT₂
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_congr	[308, 1]	[333, 25]	rw [hS]	case mpr.seq.hS S₁ S₂ T₁ T₂ : Stmt hS✝ : S₁ ~ S₂ hS : ∀ (s t : State), (S₁, s) ⟹ t ↔ (S₂, s) ⟹ t hT : T₁ ~ T₂ s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ (S₁, s) ⟹ ?m.68939 hT s t u hS₂ hT₂	case mpr.seq.hS S₁ S₂ T₁ T₂ : Stmt hS✝ : S₁ ~ S₂ hS : ∀ (s t : State), (S₁, s) ⟹ t ↔ (S₂, s) ⟹ t hT : T₁ ~ T₂ s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ (S₂, s) ⟹ ?m.68939 hT s t u hS₂ hT₂ S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ ⊢ T₁ ~ T₂ → (s t u : State) → (S₂, s) ⟹ u → (T₂, u) ⟹ t → State
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_congr	[308, 1]	[333, 25]	assumption	case mpr.seq.hS S₁ S₂ T₁ T₂ : Stmt hS✝ : S₁ ~ S₂ hS : ∀ (s t : State), (S₁, s) ⟹ t ↔ (S₂, s) ⟹ t hT : T₁ ~ T₂ s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ (S₂, s) ⟹ ?m.68939 hT s t u hS₂ hT₂ S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ ⊢ T₁ ~ T₂ → (s t u : State) → (S₂, s) ⟹ u → (T₂, u) ⟹ t → State	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_congr	[308, 1]	[333, 25]	rw [BigStepEquiv] at hT	case mpr.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ (T₁, u) ⟹ t	case mpr.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : ∀ (s t : State), (T₁, s) ⟹ t ↔ (T₂, s) ⟹ t s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ (T₁, u) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_congr	[308, 1]	[333, 25]	rw [hT]	case mpr.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : ∀ (s t : State), (T₁, s) ⟹ t ↔ (T₂, s) ⟹ t s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ (T₁, u) ⟹ t	case mpr.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : ∀ (s t : State), (T₁, s) ⟹ t ↔ (T₂, s) ⟹ t s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ (T₂, u) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.seq_congr	[308, 1]	[333, 25]	assumption	case mpr.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : ∀ (s t : State), (T₁, s) ⟹ t ↔ (T₂, s) ⟹ t s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ (T₂, u) ⟹ t	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.if_congr	[335, 1]	[367, 25]	intro s t	B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ ⊢ Stmt.ifThenElse B S₁ T₁ ~ Stmt.ifThenElse B S₂ T₂	B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (Stmt.ifThenElse B S₁ T₁, s) ⟹ t ↔ (Stmt.ifThenElse B S₂ T₂, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.if_congr	[335, 1]	[367, 25]	apply Iff.intro	B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (Stmt.ifThenElse B S₁ T₁, s) ⟹ t ↔ (Stmt.ifThenElse B S₂ T₂, s) ⟹ t	case mp B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (Stmt.ifThenElse B S₁ T₁, s) ⟹ t → (Stmt.ifThenElse B S₂ T₂, s) ⟹ t case mpr B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (Stmt.ifThenElse B S₂ T₂, s) ⟹ t → (Stmt.ifThenElse B S₁ T₁, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.if_congr	[335, 1]	[367, 25]	{ intro hif cases hif with \| if_true _ _ _ _ _ hB hS₁ => apply BigStep.if_true { assumption } { rw [BigStepEquiv] at hS rw [← hS] assumption } \| if_false _ _ _ _ _ hB hT₁ => apply BigStep.if_false { assumption } { rw [BigStepEquiv] at hT rw [← hT] assumption } }	case mp B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (Stmt.ifThenElse B S₁ T₁, s) ⟹ t → (Stmt.ifThenElse B S₂ T₂, s) ⟹ t case mpr B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (Stmt.ifThenElse B S₂ T₂, s) ⟹ t → (Stmt.ifThenElse B S₁ T₁, s) ⟹ t	case mpr B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (Stmt.ifThenElse B S₂ T₂, s) ⟹ t → (Stmt.ifThenElse B S₁ T₁, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.if_congr	[335, 1]	[367, 25]	{ intro hif cases hif with \| if_true _ _ _ _ _ hB hS₂ => apply BigStep.if_true { assumption } { rw [BigStepEquiv] at hS rw [hS] assumption } \| if_false _ _ _ _ _ hB hT₂ => apply BigStep.if_false { assumption } { rw [BigStepEquiv] at hT rw [hT] assumption } }	case mpr B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (Stmt.ifThenElse B S₂ T₂, s) ⟹ t → (Stmt.ifThenElse B S₁ T₁, s) ⟹ t	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.if_congr	[335, 1]	[367, 25]	intro hif	case mp B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (Stmt.ifThenElse B S₁ T₁, s) ⟹ t → (Stmt.ifThenElse B S₂ T₂, s) ⟹ t	case mp B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hif : (Stmt.ifThenElse B S₁ T₁, s) ⟹ t ⊢ (Stmt.ifThenElse B S₂ T₂, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.if_congr	[335, 1]	[367, 25]	cases hif with \| if_true _ _ _ _ _ hB hS₁ => apply BigStep.if_true { assumption } { rw [BigStepEquiv] at hS rw [← hS] assumption } \| if_false _ _ _ _ _ hB hT₁ => apply BigStep.if_false { assumption } { rw [BigStepEquiv] at hT rw [← hT] assumption }	case mp B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hif : (Stmt.ifThenElse B S₁ T₁, s) ⟹ t ⊢ (Stmt.ifThenElse B S₂ T₂, s) ⟹ t	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.if_congr	[335, 1]	[367, 25]	apply BigStep.if_true	case mp.if_true B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hB : B s hS₁ : (S₁, s) ⟹ t ⊢ (Stmt.ifThenElse B S₂ T₂, s) ⟹ t	case mp.if_true.hcond B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hB : B s hS₁ : (S₁, s) ⟹ t ⊢ B s case mp.if_true.hbody B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hB : B s hS₁ : (S₁, s) ⟹ t ⊢ (S₂, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.if_congr	[335, 1]	[367, 25]	{ assumption }	case mp.if_true.hcond B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hB : B s hS₁ : (S₁, s) ⟹ t ⊢ B s case mp.if_true.hbody B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hB : B s hS₁ : (S₁, s) ⟹ t ⊢ (S₂, s) ⟹ t	case mp.if_true.hbody B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hB : B s hS₁ : (S₁, s) ⟹ t ⊢ (S₂, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.if_congr	[335, 1]	[367, 25]	{ rw [BigStepEquiv] at hS rw [← hS] assumption }	case mp.if_true.hbody B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hB : B s hS₁ : (S₁, s) ⟹ t ⊢ (S₂, s) ⟹ t	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.if_congr	[335, 1]	[367, 25]	assumption	case mp.if_true.hcond B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hB : B s hS₁ : (S₁, s) ⟹ t ⊢ B s	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.if_congr	[335, 1]	[367, 25]	rw [BigStepEquiv] at hS	case mp.if_true.hbody B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hB : B s hS₁ : (S₁, s) ⟹ t ⊢ (S₂, s) ⟹ t	case mp.if_true.hbody B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : ∀ (s t : State), (S₁, s) ⟹ t ↔ (S₂, s) ⟹ t hT : T₁ ~ T₂ s t : State hB : B s hS₁ : (S₁, s) ⟹ t ⊢ (S₂, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.if_congr	[335, 1]	[367, 25]	rw [← hS]	case mp.if_true.hbody B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : ∀ (s t : State), (S₁, s) ⟹ t ↔ (S₂, s) ⟹ t hT : T₁ ~ T₂ s t : State hB : B s hS₁ : (S₁, s) ⟹ t ⊢ (S₂, s) ⟹ t	case mp.if_true.hbody B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : ∀ (s t : State), (S₁, s) ⟹ t ↔ (S₂, s) ⟹ t hT : T₁ ~ T₂ s t : State hB : B s hS₁ : (S₁, s) ⟹ t ⊢ (S₁, s) ⟹ t
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.if_congr	[335, 1]	[367, 25]	assumption	case mp.if_true.hbody B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : ∀ (s t : State), (S₁, s) ⟹ t ↔ (S₂, s) ⟹ t hT : T₁ ~ T₂ s t : State hB : B s hS₁ : (S₁, s) ⟹ t ⊢ (S₁, s) ⟹ t	no goals
https://github.com/BrownCS1951x/fpv2023.git	9aaf6b5c454aa9a70fc4e6807adf3123b001ea66	LoVe/Labs/Lab6Solution.lean	LoVe.BigStepEquiv.if_congr	[335, 1]	[367, 25]	apply BigStep.if_false	case mp.if_false B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hB : ¬B s hT₁ : (T₁, s) ⟹ t ⊢ (Stmt.ifThenElse B S₂ T₂, s) ⟹ t	case mp.if_false.hcond B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hB : ¬B s hT₁ : (T₁, s) ⟹ t ⊢ ¬B s case mp.if_false.hbody B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hB : ¬B s hT₁ : (T₁, s) ⟹ t ⊢ (T₂, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.GCL.BigStep_choice

[147, 9]

[164, 23]

cases hex with | intro hless hstep => apply BigStep.choice <;> assumption

case mpr.intro Ss : List Stmt s t : State i : ℕ hex : ∃ hless, (Ss[i], s) ⟹ t ⊢ (Stmt.choice Ss, s) ⟹ t

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.GCL.BigStep_choice

[147, 9]

[164, 23]

apply BigStep.choice <;> assumption

case mpr.intro.intro Ss : List Stmt s t : State i : ℕ hless : i < List.length Ss hstep : (Ss[i], s) ⟹ t ⊢ (Stmt.choice Ss, s) ⟹ t

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.refl

[213, 1]

[217, 11]

rfl

S : Stmt s t : State ⊢ (S, s) ⟹ t ↔ (S, s) ⟹ t

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.skip_assign_id

[234, 1]

[244, 17]

intro s t

x : String ⊢ (Stmt.assign x fun s => s x) ~ Stmt.skip

x : String s t : State ⊢ (Stmt.assign x fun s => s x, s) ⟹ t ↔ (Stmt.skip, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.skip_assign_id

[234, 1]

[244, 17]

apply Iff.intro

x : String s t : State ⊢ (Stmt.assign x fun s => s x, s) ⟹ t ↔ (Stmt.skip, s) ⟹ t

case mp x : String s t : State ⊢ (Stmt.assign x fun s => s x, s) ⟹ t → (Stmt.skip, s) ⟹ t case mpr x : String s t : State ⊢ (Stmt.skip, s) ⟹ t → (Stmt.assign x fun s => s x, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.skip_assign_id

[234, 1]

[244, 17]

{ intro hasn cases hasn simp [*] }

case mp x : String s t : State ⊢ (Stmt.assign x fun s => s x, s) ⟹ t → (Stmt.skip, s) ⟹ t case mpr x : String s t : State ⊢ (Stmt.skip, s) ⟹ t → (Stmt.assign x fun s => s x, s) ⟹ t

case mpr x : String s t : State ⊢ (Stmt.skip, s) ⟹ t → (Stmt.assign x fun s => s x, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.skip_assign_id

[234, 1]

[244, 17]

{ intro hskip cases hskip simp [*] }

case mpr x : String s t : State ⊢ (Stmt.skip, s) ⟹ t → (Stmt.assign x fun s => s x, s) ⟹ t

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.skip_assign_id

[234, 1]

[244, 17]

intro hasn

case mp x : String s t : State ⊢ (Stmt.assign x fun s => s x, s) ⟹ t → (Stmt.skip, s) ⟹ t

case mp x : String s t : State hasn : (Stmt.assign x fun s => s x, s) ⟹ t ⊢ (Stmt.skip, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.skip_assign_id

[234, 1]

[244, 17]

cases hasn

case mp x : String s t : State hasn : (Stmt.assign x fun s => s x, s) ⟹ t ⊢ (Stmt.skip, s) ⟹ t

case mp.assign x : String s : State ⊢ (Stmt.skip, s) ⟹ State.update x ((fun s => s x) s) s

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.skip_assign_id

[234, 1]

[244, 17]

simp [*]

case mp.assign x : String s : State ⊢ (Stmt.skip, s) ⟹ State.update x ((fun s => s x) s) s

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.skip_assign_id

[234, 1]

[244, 17]

intro hskip

case mpr x : String s t : State ⊢ (Stmt.skip, s) ⟹ t → (Stmt.assign x fun s => s x, s) ⟹ t

case mpr x : String s t : State hskip : (Stmt.skip, s) ⟹ t ⊢ (Stmt.assign x fun s => s x, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.skip_assign_id

[234, 1]

[244, 17]

cases hskip

case mpr x : String s t : State hskip : (Stmt.skip, s) ⟹ t ⊢ (Stmt.assign x fun s => s x, s) ⟹ t

case mpr.skip x : String s : State ⊢ (Stmt.assign x fun s => s x, s) ⟹ s

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.skip_assign_id

[234, 1]

[244, 17]

simp [*]

case mpr.skip x : String s : State ⊢ (Stmt.assign x fun s => s x, s) ⟹ s

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_skip_left

[246, 1]

[259, 23]

intro s t

S : Stmt ⊢ Stmt.skip; S ~ S

S : Stmt s t : State ⊢ (Stmt.skip; S, s) ⟹ t ↔ (S, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_skip_left

[246, 1]

[259, 23]

apply Iff.intro

S : Stmt s t : State ⊢ (Stmt.skip; S, s) ⟹ t ↔ (S, s) ⟹ t

case mp S : Stmt s t : State ⊢ (Stmt.skip; S, s) ⟹ t → (S, s) ⟹ t case mpr S : Stmt s t : State ⊢ (S, s) ⟹ t → (Stmt.skip; S, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_skip_left

[246, 1]

[259, 23]

{ intro hseq cases hseq with | seq _ _ _ u _ hs hS => cases hs assumption }

case mp S : Stmt s t : State ⊢ (Stmt.skip; S, s) ⟹ t → (S, s) ⟹ t case mpr S : Stmt s t : State ⊢ (S, s) ⟹ t → (Stmt.skip; S, s) ⟹ t

case mpr S : Stmt s t : State ⊢ (S, s) ⟹ t → (Stmt.skip; S, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_skip_left

[246, 1]

[259, 23]

{ intro hS apply BigStep.seq { apply BigStep.skip } { assumption } }

case mpr S : Stmt s t : State ⊢ (S, s) ⟹ t → (Stmt.skip; S, s) ⟹ t

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_skip_left

[246, 1]

[259, 23]

intro hseq

case mp S : Stmt s t : State ⊢ (Stmt.skip; S, s) ⟹ t → (S, s) ⟹ t

case mp S : Stmt s t : State hseq : (Stmt.skip; S, s) ⟹ t ⊢ (S, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_skip_left

[246, 1]

[259, 23]

cases hseq with | seq _ _ _ u _ hs hS => cases hs assumption

case mp S : Stmt s t : State hseq : (Stmt.skip; S, s) ⟹ t ⊢ (S, s) ⟹ t

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_skip_left

[246, 1]

[259, 23]

cases hs

case mp.seq S : Stmt s t u : State hs : (Stmt.skip, s) ⟹ u hS : (S, u) ⟹ t ⊢ (S, s) ⟹ t

case mp.seq.skip S : Stmt s t : State hS : (S, s) ⟹ t ⊢ (S, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_skip_left

[246, 1]

[259, 23]

assumption

case mp.seq.skip S : Stmt s t : State hS : (S, s) ⟹ t ⊢ (S, s) ⟹ t

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_skip_left

[246, 1]

[259, 23]

intro hS

case mpr S : Stmt s t : State ⊢ (S, s) ⟹ t → (Stmt.skip; S, s) ⟹ t

case mpr S : Stmt s t : State hS : (S, s) ⟹ t ⊢ (Stmt.skip; S, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_skip_left

[246, 1]

[259, 23]

apply BigStep.seq

case mpr S : Stmt s t : State hS : (S, s) ⟹ t ⊢ (Stmt.skip; S, s) ⟹ t

case mpr.hS S : Stmt s t : State hS : (S, s) ⟹ t ⊢ (Stmt.skip, s) ⟹ ?mpr.t case mpr.hT S : Stmt s t : State hS : (S, s) ⟹ t ⊢ (S, ?mpr.t) ⟹ t case mpr.t S : Stmt s t : State hS : (S, s) ⟹ t ⊢ State

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_skip_left

[246, 1]

[259, 23]

{ apply BigStep.skip }

case mpr.hS S : Stmt s t : State hS : (S, s) ⟹ t ⊢ (Stmt.skip, s) ⟹ ?mpr.t case mpr.hT S : Stmt s t : State hS : (S, s) ⟹ t ⊢ (S, ?mpr.t) ⟹ t case mpr.t S : Stmt s t : State hS : (S, s) ⟹ t ⊢ State

case mpr.hT S : Stmt s t : State hS : (S, s) ⟹ t ⊢ (S, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_skip_left

[246, 1]

[259, 23]

{ assumption }

case mpr.hT S : Stmt s t : State hS : (S, s) ⟹ t ⊢ (S, s) ⟹ t

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_skip_left

[246, 1]

[259, 23]

apply BigStep.skip

case mpr.hS S : Stmt s t : State hS : (S, s) ⟹ t ⊢ (Stmt.skip, s) ⟹ ?mpr.t

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_skip_left

[246, 1]

[259, 23]

assumption

case mpr.hT S : Stmt s t : State hS : (S, s) ⟹ t ⊢ (S, s) ⟹ t

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_skip_right

[261, 1]

[274, 31]

intro s t

S : Stmt ⊢ S; Stmt.skip ~ S

S : Stmt s t : State ⊢ (S; Stmt.skip, s) ⟹ t ↔ (S, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_skip_right

[261, 1]

[274, 31]

apply Iff.intro

S : Stmt s t : State ⊢ (S; Stmt.skip, s) ⟹ t ↔ (S, s) ⟹ t

case mp S : Stmt s t : State ⊢ (S; Stmt.skip, s) ⟹ t → (S, s) ⟹ t case mpr S : Stmt s t : State ⊢ (S, s) ⟹ t → (S; Stmt.skip, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_skip_right

[261, 1]

[274, 31]

{ intro hseq cases hseq with | seq _ _ _ u _ hS hs => cases hs assumption }

case mp S : Stmt s t : State ⊢ (S; Stmt.skip, s) ⟹ t → (S, s) ⟹ t case mpr S : Stmt s t : State ⊢ (S, s) ⟹ t → (S; Stmt.skip, s) ⟹ t

case mpr S : Stmt s t : State ⊢ (S, s) ⟹ t → (S; Stmt.skip, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_skip_right

[261, 1]

[274, 31]

{ intro h apply BigStep.seq { assumption } { apply BigStep.skip } }

case mpr S : Stmt s t : State ⊢ (S, s) ⟹ t → (S; Stmt.skip, s) ⟹ t

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_skip_right

[261, 1]

[274, 31]

intro hseq

case mp S : Stmt s t : State ⊢ (S; Stmt.skip, s) ⟹ t → (S, s) ⟹ t

case mp S : Stmt s t : State hseq : (S; Stmt.skip, s) ⟹ t ⊢ (S, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_skip_right

[261, 1]

[274, 31]

cases hseq with | seq _ _ _ u _ hS hs => cases hs assumption

case mp S : Stmt s t : State hseq : (S; Stmt.skip, s) ⟹ t ⊢ (S, s) ⟹ t

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_skip_right

[261, 1]

[274, 31]

cases hs

case mp.seq S : Stmt s t u : State hS : (S, s) ⟹ u hs : (Stmt.skip, u) ⟹ t ⊢ (S, s) ⟹ t

case mp.seq.skip S : Stmt s t : State hS : (S, s) ⟹ t ⊢ (S, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_skip_right

[261, 1]

[274, 31]

assumption

case mp.seq.skip S : Stmt s t : State hS : (S, s) ⟹ t ⊢ (S, s) ⟹ t

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_skip_right

[261, 1]

[274, 31]

intro h

case mpr S : Stmt s t : State ⊢ (S, s) ⟹ t → (S; Stmt.skip, s) ⟹ t

case mpr S : Stmt s t : State h : (S, s) ⟹ t ⊢ (S; Stmt.skip, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_skip_right

[261, 1]

[274, 31]

apply BigStep.seq

case mpr S : Stmt s t : State h : (S, s) ⟹ t ⊢ (S; Stmt.skip, s) ⟹ t

case mpr.hS S : Stmt s t : State h : (S, s) ⟹ t ⊢ (S, s) ⟹ ?mpr.t case mpr.hT S : Stmt s t : State h : (S, s) ⟹ t ⊢ (Stmt.skip, ?mpr.t) ⟹ t case mpr.t S : Stmt s t : State h : (S, s) ⟹ t ⊢ State

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_skip_right

[261, 1]

[274, 31]

{ assumption }

case mpr.hS S : Stmt s t : State h : (S, s) ⟹ t ⊢ (S, s) ⟹ ?mpr.t case mpr.hT S : Stmt s t : State h : (S, s) ⟹ t ⊢ (Stmt.skip, ?mpr.t) ⟹ t case mpr.t S : Stmt s t : State h : (S, s) ⟹ t ⊢ State

case mpr.hT S : Stmt s t : State h : (S, s) ⟹ t ⊢ (Stmt.skip, t) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_skip_right

[261, 1]

[274, 31]

{ apply BigStep.skip }

case mpr.hT S : Stmt s t : State h : (S, s) ⟹ t ⊢ (Stmt.skip, t) ⟹ t

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_skip_right

[261, 1]

[274, 31]

assumption

case mpr.hS S : Stmt s t : State h : (S, s) ⟹ t ⊢ (S, s) ⟹ ?mpr.t

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_skip_right

[261, 1]

[274, 31]

apply BigStep.skip

case mpr.hT S : Stmt s t : State h : (S, s) ⟹ t ⊢ (Stmt.skip, t) ⟹ t

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.if_seq_while_skip

[276, 1]

[302, 29]

intro s t

B : State → Prop S : Stmt ⊢ Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip ~ Stmt.whileDo B S

B : State → Prop S : Stmt s t : State ⊢ (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⟹ t ↔ (Stmt.whileDo B S, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.if_seq_while_skip

[276, 1]

[302, 29]

apply Iff.intro

B : State → Prop S : Stmt s t : State ⊢ (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⟹ t ↔ (Stmt.whileDo B S, s) ⟹ t

case mp B : State → Prop S : Stmt s t : State ⊢ (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⟹ t → (Stmt.whileDo B S, s) ⟹ t case mpr B : State → Prop S : Stmt s t : State ⊢ (Stmt.whileDo B S, s) ⟹ t → (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.if_seq_while_skip

[276, 1]

[302, 29]

{ intro hif cases hif with | if_true _ _ _ _ _ hB hseq => cases hseq with | seq _ _ _ u _ hS hT => apply BigStep.while_true <;> assumption | if_false _ _ _ _ _ hB hskip => cases hskip apply BigStep.while_false assumption }

case mp B : State → Prop S : Stmt s t : State ⊢ (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⟹ t → (Stmt.whileDo B S, s) ⟹ t case mpr B : State → Prop S : Stmt s t : State ⊢ (Stmt.whileDo B S, s) ⟹ t → (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⟹ t

case mpr B : State → Prop S : Stmt s t : State ⊢ (Stmt.whileDo B S, s) ⟹ t → (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.if_seq_while_skip

[276, 1]

[302, 29]

{ intro hwhile cases hwhile with | while_true _ _ _ u _ hB hS hw => apply BigStep.if_true exact hB apply BigStep.seq <;> assumption | while_false _ _ _ hB => apply BigStep.if_false exact hB apply BigStep.skip }

case mpr B : State → Prop S : Stmt s t : State ⊢ (Stmt.whileDo B S, s) ⟹ t → (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⟹ t

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.if_seq_while_skip

[276, 1]

[302, 29]

intro hif

case mp B : State → Prop S : Stmt s t : State ⊢ (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⟹ t → (Stmt.whileDo B S, s) ⟹ t

case mp B : State → Prop S : Stmt s t : State hif : (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⟹ t ⊢ (Stmt.whileDo B S, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.if_seq_while_skip

[276, 1]

[302, 29]

cases hif with | if_true _ _ _ _ _ hB hseq => cases hseq with | seq _ _ _ u _ hS hT => apply BigStep.while_true <;> assumption | if_false _ _ _ _ _ hB hskip => cases hskip apply BigStep.while_false assumption

case mp B : State → Prop S : Stmt s t : State hif : (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⟹ t ⊢ (Stmt.whileDo B S, s) ⟹ t

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.if_seq_while_skip

[276, 1]

[302, 29]

cases hseq with | seq _ _ _ u _ hS hT => apply BigStep.while_true <;> assumption

case mp.if_true B : State → Prop S : Stmt s t : State hB : B s hseq : (S; Stmt.whileDo B S, s) ⟹ t ⊢ (Stmt.whileDo B S, s) ⟹ t

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.if_seq_while_skip

[276, 1]

[302, 29]

apply BigStep.while_true <;> assumption

case mp.if_true.seq B : State → Prop S : Stmt s t : State hB : B s u : State hS : (S, s) ⟹ u hT : (Stmt.whileDo B S, u) ⟹ t ⊢ (Stmt.whileDo B S, s) ⟹ t

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.if_seq_while_skip

[276, 1]

[302, 29]

cases hskip

case mp.if_false B : State → Prop S : Stmt s t : State hB : ¬B s hskip : (Stmt.skip, s) ⟹ t ⊢ (Stmt.whileDo B S, s) ⟹ t

case mp.if_false.skip B : State → Prop S : Stmt s : State hB : ¬B s ⊢ (Stmt.whileDo B S, s) ⟹ s

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.if_seq_while_skip

[276, 1]

[302, 29]

apply BigStep.while_false

case mp.if_false.skip B : State → Prop S : Stmt s : State hB : ¬B s ⊢ (Stmt.whileDo B S, s) ⟹ s

case mp.if_false.skip.hcond B : State → Prop S : Stmt s : State hB : ¬B s ⊢ ¬B s

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.if_seq_while_skip

[276, 1]

[302, 29]

assumption

case mp.if_false.skip.hcond B : State → Prop S : Stmt s : State hB : ¬B s ⊢ ¬B s

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.if_seq_while_skip

[276, 1]

[302, 29]

intro hwhile

case mpr B : State → Prop S : Stmt s t : State ⊢ (Stmt.whileDo B S, s) ⟹ t → (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⟹ t

case mpr B : State → Prop S : Stmt s t : State hwhile : (Stmt.whileDo B S, s) ⟹ t ⊢ (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.if_seq_while_skip

[276, 1]

[302, 29]

cases hwhile with | while_true _ _ _ u _ hB hS hw => apply BigStep.if_true exact hB apply BigStep.seq <;> assumption | while_false _ _ _ hB => apply BigStep.if_false exact hB apply BigStep.skip

case mpr B : State → Prop S : Stmt s t : State hwhile : (Stmt.whileDo B S, s) ⟹ t ⊢ (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⟹ t

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.if_seq_while_skip

[276, 1]

[302, 29]

apply BigStep.if_true

case mpr.while_true B : State → Prop S : Stmt s t u : State hB : B s hS : (S, s) ⟹ u hw : (Stmt.whileDo B S, u) ⟹ t ⊢ (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⟹ t

case mpr.while_true.hcond B : State → Prop S : Stmt s t u : State hB : B s hS : (S, s) ⟹ u hw : (Stmt.whileDo B S, u) ⟹ t ⊢ B s case mpr.while_true.hbody B : State → Prop S : Stmt s t u : State hB : B s hS : (S, s) ⟹ u hw : (Stmt.whileDo B S, u) ⟹ t ⊢ (S; Stmt.whileDo B S, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.if_seq_while_skip

[276, 1]

[302, 29]

exact hB

case mpr.while_true.hcond B : State → Prop S : Stmt s t u : State hB : B s hS : (S, s) ⟹ u hw : (Stmt.whileDo B S, u) ⟹ t ⊢ B s case mpr.while_true.hbody B : State → Prop S : Stmt s t u : State hB : B s hS : (S, s) ⟹ u hw : (Stmt.whileDo B S, u) ⟹ t ⊢ (S; Stmt.whileDo B S, s) ⟹ t

case mpr.while_true.hbody B : State → Prop S : Stmt s t u : State hB : B s hS : (S, s) ⟹ u hw : (Stmt.whileDo B S, u) ⟹ t ⊢ (S; Stmt.whileDo B S, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.if_seq_while_skip

[276, 1]

[302, 29]

apply BigStep.seq <;> assumption

case mpr.while_true.hbody B : State → Prop S : Stmt s t u : State hB : B s hS : (S, s) ⟹ u hw : (Stmt.whileDo B S, u) ⟹ t ⊢ (S; Stmt.whileDo B S, s) ⟹ t

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.if_seq_while_skip

[276, 1]

[302, 29]

apply BigStep.if_false

case mpr.while_false B : State → Prop S : Stmt s : State hB : ¬B s ⊢ (Stmt.ifThenElse B (S; Stmt.whileDo B S) Stmt.skip, s) ⟹ s

case mpr.while_false.hcond B : State → Prop S : Stmt s : State hB : ¬B s ⊢ ¬B s case mpr.while_false.hbody B : State → Prop S : Stmt s : State hB : ¬B s ⊢ (Stmt.skip, s) ⟹ s

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.if_seq_while_skip

[276, 1]

[302, 29]

exact hB

case mpr.while_false.hcond B : State → Prop S : Stmt s : State hB : ¬B s ⊢ ¬B s case mpr.while_false.hbody B : State → Prop S : Stmt s : State hB : ¬B s ⊢ (Stmt.skip, s) ⟹ s

case mpr.while_false.hbody B : State → Prop S : Stmt s : State hB : ¬B s ⊢ (Stmt.skip, s) ⟹ s

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.if_seq_while_skip

[276, 1]

[302, 29]

apply BigStep.skip

case mpr.while_false.hbody B : State → Prop S : Stmt s : State hB : ¬B s ⊢ (Stmt.skip, s) ⟹ s

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_congr

[308, 1]

[333, 25]

intro s t

S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ ⊢ S₁; T₁ ~ S₂; T₂

S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (S₁; T₁, s) ⟹ t ↔ (S₂; T₂, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_congr

[308, 1]

[333, 25]

apply Iff.intro

S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (S₁; T₁, s) ⟹ t ↔ (S₂; T₂, s) ⟹ t

case mp S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (S₁; T₁, s) ⟹ t → (S₂; T₂, s) ⟹ t case mpr S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (S₂; T₂, s) ⟹ t → (S₁; T₁, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_congr

[308, 1]

[333, 25]

{ intro hseq cases hseq with | seq _ _ _ u _ hS₁ hT₁ => apply BigStep.seq { rw [BigStepEquiv] at hS rw [← hS] assumption } { rw [BigStepEquiv] at hT rw [← hT] assumption } }

case mp S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (S₁; T₁, s) ⟹ t → (S₂; T₂, s) ⟹ t case mpr S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (S₂; T₂, s) ⟹ t → (S₁; T₁, s) ⟹ t

case mpr S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (S₂; T₂, s) ⟹ t → (S₁; T₁, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_congr

[308, 1]

[333, 25]

{ intro hseq cases hseq with | seq _ _ _ u _ hS₂ hT₂ => apply BigStep.seq { rw [BigStepEquiv] at hS rw [hS] assumption } { rw [BigStepEquiv] at hT rw [hT] assumption } }

case mpr S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (S₂; T₂, s) ⟹ t → (S₁; T₁, s) ⟹ t

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_congr

[308, 1]

[333, 25]

intro hseq

case mp S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (S₁; T₁, s) ⟹ t → (S₂; T₂, s) ⟹ t

case mp S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hseq : (S₁; T₁, s) ⟹ t ⊢ (S₂; T₂, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_congr

[308, 1]

[333, 25]

cases hseq with | seq _ _ _ u _ hS₁ hT₁ => apply BigStep.seq { rw [BigStepEquiv] at hS rw [← hS] assumption } { rw [BigStepEquiv] at hT rw [← hT] assumption }

case mp S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hseq : (S₁; T₁, s) ⟹ t ⊢ (S₂; T₂, s) ⟹ t

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_congr

[308, 1]

[333, 25]

apply BigStep.seq

case mp.seq S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ (S₂; T₂, s) ⟹ t

case mp.seq.hS S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ (S₂, s) ⟹ ?mp.seq.t case mp.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ (T₂, ?mp.seq.t) ⟹ t case mp.seq.t S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ State

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_congr

[308, 1]

[333, 25]

{ rw [BigStepEquiv] at hS rw [← hS] assumption }

case mp.seq.hS S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ (S₂, s) ⟹ ?mp.seq.t case mp.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ (T₂, ?mp.seq.t) ⟹ t case mp.seq.t S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ State

case mp.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ (T₂, u) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_congr

[308, 1]

[333, 25]

{ rw [BigStepEquiv] at hT rw [← hT] assumption }

case mp.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ (T₂, u) ⟹ t

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_congr

[308, 1]

[333, 25]

rw [BigStepEquiv] at hS

case mp.seq.hS S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ (S₂, s) ⟹ ?mp.seq.t

case mp.seq.hS S₁ S₂ T₁ T₂ : Stmt hS✝ : S₁ ~ S₂ hS : ∀ (s t : State), (S₁, s) ⟹ t ↔ (S₂, s) ⟹ t hT : T₁ ~ T₂ s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ (S₂, s) ⟹ ?m.68459 hT s t u hS₁ hT₁

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_congr

[308, 1]

[333, 25]

rw [← hS]

case mp.seq.hS S₁ S₂ T₁ T₂ : Stmt hS✝ : S₁ ~ S₂ hS : ∀ (s t : State), (S₁, s) ⟹ t ↔ (S₂, s) ⟹ t hT : T₁ ~ T₂ s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ (S₂, s) ⟹ ?m.68459 hT s t u hS₁ hT₁

case mp.seq.hS S₁ S₂ T₁ T₂ : Stmt hS✝ : S₁ ~ S₂ hS : ∀ (s t : State), (S₁, s) ⟹ t ↔ (S₂, s) ⟹ t hT : T₁ ~ T₂ s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ (S₁, s) ⟹ ?m.68459 hT s t u hS₁ hT₁ S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ ⊢ T₁ ~ T₂ → (s t u : State) → (S₁, s) ⟹ u → (T₁, u) ⟹ t → State

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_congr

[308, 1]

[333, 25]

assumption

case mp.seq.hS S₁ S₂ T₁ T₂ : Stmt hS✝ : S₁ ~ S₂ hS : ∀ (s t : State), (S₁, s) ⟹ t ↔ (S₂, s) ⟹ t hT : T₁ ~ T₂ s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ (S₁, s) ⟹ ?m.68459 hT s t u hS₁ hT₁ S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ ⊢ T₁ ~ T₂ → (s t u : State) → (S₁, s) ⟹ u → (T₁, u) ⟹ t → State

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_congr

[308, 1]

[333, 25]

rw [BigStepEquiv] at hT

case mp.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ (T₂, u) ⟹ t

case mp.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : ∀ (s t : State), (T₁, s) ⟹ t ↔ (T₂, s) ⟹ t s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ (T₂, u) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_congr

[308, 1]

[333, 25]

rw [← hT]

case mp.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : ∀ (s t : State), (T₁, s) ⟹ t ↔ (T₂, s) ⟹ t s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ (T₂, u) ⟹ t

case mp.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : ∀ (s t : State), (T₁, s) ⟹ t ↔ (T₂, s) ⟹ t s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ (T₁, u) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_congr

[308, 1]

[333, 25]

assumption

case mp.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : ∀ (s t : State), (T₁, s) ⟹ t ↔ (T₂, s) ⟹ t s t u : State hS₁ : (S₁, s) ⟹ u hT₁ : (T₁, u) ⟹ t ⊢ (T₁, u) ⟹ t

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_congr

[308, 1]

[333, 25]

intro hseq

case mpr S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (S₂; T₂, s) ⟹ t → (S₁; T₁, s) ⟹ t

case mpr S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hseq : (S₂; T₂, s) ⟹ t ⊢ (S₁; T₁, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_congr

[308, 1]

[333, 25]

cases hseq with | seq _ _ _ u _ hS₂ hT₂ => apply BigStep.seq { rw [BigStepEquiv] at hS rw [hS] assumption } { rw [BigStepEquiv] at hT rw [hT] assumption }

case mpr S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hseq : (S₂; T₂, s) ⟹ t ⊢ (S₁; T₁, s) ⟹ t

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_congr

[308, 1]

[333, 25]

apply BigStep.seq

case mpr.seq S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ (S₁; T₁, s) ⟹ t

case mpr.seq.hS S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ (S₁, s) ⟹ ?mpr.seq.t case mpr.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ (T₁, ?mpr.seq.t) ⟹ t case mpr.seq.t S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ State

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_congr

[308, 1]

[333, 25]

{ rw [BigStepEquiv] at hS rw [hS] assumption }

case mpr.seq.hS S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ (S₁, s) ⟹ ?mpr.seq.t case mpr.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ (T₁, ?mpr.seq.t) ⟹ t case mpr.seq.t S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ State

case mpr.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ (T₁, u) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_congr

[308, 1]

[333, 25]

{ rw [BigStepEquiv] at hT rw [hT] assumption }

case mpr.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ (T₁, u) ⟹ t

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_congr

[308, 1]

[333, 25]

rw [BigStepEquiv] at hS

case mpr.seq.hS S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ (S₁, s) ⟹ ?mpr.seq.t

case mpr.seq.hS S₁ S₂ T₁ T₂ : Stmt hS✝ : S₁ ~ S₂ hS : ∀ (s t : State), (S₁, s) ⟹ t ↔ (S₂, s) ⟹ t hT : T₁ ~ T₂ s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ (S₁, s) ⟹ ?m.68939 hT s t u hS₂ hT₂

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_congr

[308, 1]

[333, 25]

rw [hS]

case mpr.seq.hS S₁ S₂ T₁ T₂ : Stmt hS✝ : S₁ ~ S₂ hS : ∀ (s t : State), (S₁, s) ⟹ t ↔ (S₂, s) ⟹ t hT : T₁ ~ T₂ s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ (S₁, s) ⟹ ?m.68939 hT s t u hS₂ hT₂

case mpr.seq.hS S₁ S₂ T₁ T₂ : Stmt hS✝ : S₁ ~ S₂ hS : ∀ (s t : State), (S₁, s) ⟹ t ↔ (S₂, s) ⟹ t hT : T₁ ~ T₂ s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ (S₂, s) ⟹ ?m.68939 hT s t u hS₂ hT₂ S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ ⊢ T₁ ~ T₂ → (s t u : State) → (S₂, s) ⟹ u → (T₂, u) ⟹ t → State

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_congr

[308, 1]

[333, 25]

assumption

case mpr.seq.hS S₁ S₂ T₁ T₂ : Stmt hS✝ : S₁ ~ S₂ hS : ∀ (s t : State), (S₁, s) ⟹ t ↔ (S₂, s) ⟹ t hT : T₁ ~ T₂ s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ (S₂, s) ⟹ ?m.68939 hT s t u hS₂ hT₂ S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ ⊢ T₁ ~ T₂ → (s t u : State) → (S₂, s) ⟹ u → (T₂, u) ⟹ t → State

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_congr

[308, 1]

[333, 25]

rw [BigStepEquiv] at hT

case mpr.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ (T₁, u) ⟹ t

case mpr.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : ∀ (s t : State), (T₁, s) ⟹ t ↔ (T₂, s) ⟹ t s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ (T₁, u) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_congr

[308, 1]

[333, 25]

rw [hT]

case mpr.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : ∀ (s t : State), (T₁, s) ⟹ t ↔ (T₂, s) ⟹ t s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ (T₁, u) ⟹ t

case mpr.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : ∀ (s t : State), (T₁, s) ⟹ t ↔ (T₂, s) ⟹ t s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ (T₂, u) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.seq_congr

[308, 1]

[333, 25]

assumption

case mpr.seq.hT S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : ∀ (s t : State), (T₁, s) ⟹ t ↔ (T₂, s) ⟹ t s t u : State hS₂ : (S₂, s) ⟹ u hT₂ : (T₂, u) ⟹ t ⊢ (T₂, u) ⟹ t

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.if_congr

[335, 1]

[367, 25]

intro s t

B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ ⊢ Stmt.ifThenElse B S₁ T₁ ~ Stmt.ifThenElse B S₂ T₂

B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (Stmt.ifThenElse B S₁ T₁, s) ⟹ t ↔ (Stmt.ifThenElse B S₂ T₂, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.if_congr

[335, 1]

[367, 25]

apply Iff.intro

B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (Stmt.ifThenElse B S₁ T₁, s) ⟹ t ↔ (Stmt.ifThenElse B S₂ T₂, s) ⟹ t

case mp B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (Stmt.ifThenElse B S₁ T₁, s) ⟹ t → (Stmt.ifThenElse B S₂ T₂, s) ⟹ t case mpr B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (Stmt.ifThenElse B S₂ T₂, s) ⟹ t → (Stmt.ifThenElse B S₁ T₁, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.if_congr

[335, 1]

[367, 25]

{ intro hif cases hif with | if_true _ _ _ _ _ hB hS₁ => apply BigStep.if_true { assumption } { rw [BigStepEquiv] at hS rw [← hS] assumption } | if_false _ _ _ _ _ hB hT₁ => apply BigStep.if_false { assumption } { rw [BigStepEquiv] at hT rw [← hT] assumption } }

case mp B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (Stmt.ifThenElse B S₁ T₁, s) ⟹ t → (Stmt.ifThenElse B S₂ T₂, s) ⟹ t case mpr B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (Stmt.ifThenElse B S₂ T₂, s) ⟹ t → (Stmt.ifThenElse B S₁ T₁, s) ⟹ t

case mpr B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (Stmt.ifThenElse B S₂ T₂, s) ⟹ t → (Stmt.ifThenElse B S₁ T₁, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.if_congr

[335, 1]

[367, 25]

{ intro hif cases hif with | if_true _ _ _ _ _ hB hS₂ => apply BigStep.if_true { assumption } { rw [BigStepEquiv] at hS rw [hS] assumption } | if_false _ _ _ _ _ hB hT₂ => apply BigStep.if_false { assumption } { rw [BigStepEquiv] at hT rw [hT] assumption } }

case mpr B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (Stmt.ifThenElse B S₂ T₂, s) ⟹ t → (Stmt.ifThenElse B S₁ T₁, s) ⟹ t

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.if_congr

[335, 1]

[367, 25]

intro hif

case mp B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State ⊢ (Stmt.ifThenElse B S₁ T₁, s) ⟹ t → (Stmt.ifThenElse B S₂ T₂, s) ⟹ t

case mp B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hif : (Stmt.ifThenElse B S₁ T₁, s) ⟹ t ⊢ (Stmt.ifThenElse B S₂ T₂, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.if_congr

[335, 1]

[367, 25]

cases hif with | if_true _ _ _ _ _ hB hS₁ => apply BigStep.if_true { assumption } { rw [BigStepEquiv] at hS rw [← hS] assumption } | if_false _ _ _ _ _ hB hT₁ => apply BigStep.if_false { assumption } { rw [BigStepEquiv] at hT rw [← hT] assumption }

case mp B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hif : (Stmt.ifThenElse B S₁ T₁, s) ⟹ t ⊢ (Stmt.ifThenElse B S₂ T₂, s) ⟹ t

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.if_congr

[335, 1]

[367, 25]

apply BigStep.if_true

case mp.if_true B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hB : B s hS₁ : (S₁, s) ⟹ t ⊢ (Stmt.ifThenElse B S₂ T₂, s) ⟹ t

case mp.if_true.hcond B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hB : B s hS₁ : (S₁, s) ⟹ t ⊢ B s case mp.if_true.hbody B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hB : B s hS₁ : (S₁, s) ⟹ t ⊢ (S₂, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.if_congr

[335, 1]

[367, 25]

{ assumption }

case mp.if_true.hcond B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hB : B s hS₁ : (S₁, s) ⟹ t ⊢ B s case mp.if_true.hbody B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hB : B s hS₁ : (S₁, s) ⟹ t ⊢ (S₂, s) ⟹ t

case mp.if_true.hbody B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hB : B s hS₁ : (S₁, s) ⟹ t ⊢ (S₂, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.if_congr

[335, 1]

[367, 25]

{ rw [BigStepEquiv] at hS rw [← hS] assumption }

case mp.if_true.hbody B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hB : B s hS₁ : (S₁, s) ⟹ t ⊢ (S₂, s) ⟹ t

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.if_congr

[335, 1]

[367, 25]

assumption

case mp.if_true.hcond B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hB : B s hS₁ : (S₁, s) ⟹ t ⊢ B s

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.if_congr

[335, 1]

[367, 25]

rw [BigStepEquiv] at hS

case mp.if_true.hbody B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hB : B s hS₁ : (S₁, s) ⟹ t ⊢ (S₂, s) ⟹ t

case mp.if_true.hbody B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : ∀ (s t : State), (S₁, s) ⟹ t ↔ (S₂, s) ⟹ t hT : T₁ ~ T₂ s t : State hB : B s hS₁ : (S₁, s) ⟹ t ⊢ (S₂, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.if_congr

[335, 1]

[367, 25]

rw [← hS]

case mp.if_true.hbody B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : ∀ (s t : State), (S₁, s) ⟹ t ↔ (S₂, s) ⟹ t hT : T₁ ~ T₂ s t : State hB : B s hS₁ : (S₁, s) ⟹ t ⊢ (S₂, s) ⟹ t

case mp.if_true.hbody B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : ∀ (s t : State), (S₁, s) ⟹ t ↔ (S₂, s) ⟹ t hT : T₁ ~ T₂ s t : State hB : B s hS₁ : (S₁, s) ⟹ t ⊢ (S₁, s) ⟹ t

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.if_congr

[335, 1]

[367, 25]

assumption

case mp.if_true.hbody B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : ∀ (s t : State), (S₁, s) ⟹ t ↔ (S₂, s) ⟹ t hT : T₁ ~ T₂ s t : State hB : B s hS₁ : (S₁, s) ⟹ t ⊢ (S₁, s) ⟹ t

no goals

https://github.com/BrownCS1951x/fpv2023.git

9aaf6b5c454aa9a70fc4e6807adf3123b001ea66

LoVe/Labs/Lab6Solution.lean

LoVe.BigStepEquiv.if_congr

[335, 1]

[367, 25]

apply BigStep.if_false

case mp.if_false B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hB : ¬B s hT₁ : (T₁, s) ⟹ t ⊢ (Stmt.ifThenElse B S₂ T₂, s) ⟹ t

case mp.if_false.hcond B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hB : ¬B s hT₁ : (T₁, s) ⟹ t ⊢ ¬B s case mp.if_false.hbody B : State → Prop S₁ S₂ T₁ T₂ : Stmt hS : S₁ ~ S₂ hT : T₁ ~ T₂ s t : State hB : ¬B s hT₁ : (T₁, s) ⟹ t ⊢ (T₂, s) ⟹ t