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https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.uniqueAux_acc_append_filter | [1075, 1] | [1134, 25] | apply funext | α : Type u_1
inst✝ : DecidableEq α
x : α
xs acc : List α
hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs)
hterm' : length xs < Nat.succ (length xs)
ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs)
ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs)
ih₃ :
uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] =
reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs))
hout : ¬x ∈ acc
this :
(fun x_1 => decide ((decide ¬x_1 ∈ acc) = true ∧ (decide ¬x_1 ∈ [x]) = true)) = fun x_1 =>
decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x])
h_mem_iff : ∀ (x_1 : α), x_1 ∈ x :: acc ↔ x_1 ∈ [x] ∨ x_1 ∈ acc
h_mem_iff_neg : ∀ (x_1 : α), ¬x_1 ∈ x :: acc ↔ ¬(x_1 ∈ [x] ∨ x_1 ∈ acc)
⊢ (fun x_1 => decide ¬x_1 ∈ x :: acc) = fun x_1 => decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x]) | case h
α : Type u_1
inst✝ : DecidableEq α
x : α
xs acc : List α
hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs)
hterm' : length xs < Nat.succ (length xs)
ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs)
ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs)
ih₃ :
uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] =
reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs))
hout : ¬x ∈ acc
this :
(fun x_1 => decide ((decide ¬x_1 ∈ acc) = true ∧ (decide ¬x_1 ∈ [x]) = true)) = fun x_1 =>
decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x])
h_mem_iff : ∀ (x_1 : α), x_1 ∈ x :: acc ↔ x_1 ∈ [x] ∨ x_1 ∈ acc
h_mem_iff_neg : ∀ (x_1 : α), ¬x_1 ∈ x :: acc ↔ ¬(x_1 ∈ [x] ∨ x_1 ∈ acc)
⊢ ∀ (x_1 : α), (decide ¬x_1 ∈ x :: acc) = decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x]) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.uniqueAux_acc_append_filter | [1075, 1] | [1134, 25] | intros a | case h
α : Type u_1
inst✝ : DecidableEq α
x : α
xs acc : List α
hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs)
hterm' : length xs < Nat.succ (length xs)
ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs)
ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs)
ih₃ :
uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] =
reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs))
hout : ¬x ∈ acc
this :
(fun x_1 => decide ((decide ¬x_1 ∈ acc) = true ∧ (decide ¬x_1 ∈ [x]) = true)) = fun x_1 =>
decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x])
h_mem_iff : ∀ (x_1 : α), x_1 ∈ x :: acc ↔ x_1 ∈ [x] ∨ x_1 ∈ acc
h_mem_iff_neg : ∀ (x_1 : α), ¬x_1 ∈ x :: acc ↔ ¬(x_1 ∈ [x] ∨ x_1 ∈ acc)
⊢ ∀ (x_1 : α), (decide ¬x_1 ∈ x :: acc) = decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x]) | case h
α : Type u_1
inst✝ : DecidableEq α
x : α
xs acc : List α
hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs)
hterm' : length xs < Nat.succ (length xs)
ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs)
ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs)
ih₃ :
uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] =
reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs))
hout : ¬x ∈ acc
this :
(fun x_1 => decide ((decide ¬x_1 ∈ acc) = true ∧ (decide ¬x_1 ∈ [x]) = true)) = fun x_1 =>
decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x])
h_mem_iff : ∀ (x_1 : α), x_1 ∈ x :: acc ↔ x_1 ∈ [x] ∨ x_1 ∈ acc
h_mem_iff_neg : ∀ (x_1 : α), ¬x_1 ∈ x :: acc ↔ ¬(x_1 ∈ [x] ∨ x_1 ∈ acc)
a : α
⊢ (decide ¬a ∈ x :: acc) = decide (¬a ∈ acc ∧ ¬a ∈ [x]) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.uniqueAux_acc_append_filter | [1075, 1] | [1134, 25] | apply Decidable.prop_eq_of_decide_eq | case h
α : Type u_1
inst✝ : DecidableEq α
x : α
xs acc : List α
hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs)
hterm' : length xs < Nat.succ (length xs)
ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs)
ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs)
ih₃ :
uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] =
reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs))
hout : ¬x ∈ acc
this :
(fun x_1 => decide ((decide ¬x_1 ∈ acc) = true ∧ (decide ¬x_1 ∈ [x]) = true)) = fun x_1 =>
decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x])
h_mem_iff : ∀ (x_1 : α), x_1 ∈ x :: acc ↔ x_1 ∈ [x] ∨ x_1 ∈ acc
h_mem_iff_neg : ∀ (x_1 : α), ¬x_1 ∈ x :: acc ↔ ¬(x_1 ∈ [x] ∨ x_1 ∈ acc)
a : α
⊢ (decide ¬a ∈ x :: acc) = decide (¬a ∈ acc ∧ ¬a ∈ [x]) | case h.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs acc : List α
hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs)
hterm' : length xs < Nat.succ (length xs)
ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs)
ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs)
ih₃ :
uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] =
reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs))
hout : ¬x ∈ acc
this :
(fun x_1 => decide ((decide ¬x_1 ∈ acc) = true ∧ (decide ¬x_1 ∈ [x]) = true)) = fun x_1 =>
decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x])
h_mem_iff : ∀ (x_1 : α), x_1 ∈ x :: acc ↔ x_1 ∈ [x] ∨ x_1 ∈ acc
h_mem_iff_neg : ∀ (x_1 : α), ¬x_1 ∈ x :: acc ↔ ¬(x_1 ∈ [x] ∨ x_1 ∈ acc)
a : α
⊢ (¬a ∈ x :: acc) = (¬a ∈ acc ∧ ¬a ∈ [x]) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.uniqueAux_acc_append_filter | [1075, 1] | [1134, 25] | rw [h_mem_iff_neg, not_or_distrib, And.comm] | case h.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs acc : List α
hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs)
hterm' : length xs < Nat.succ (length xs)
ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs)
ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs)
ih₃ :
uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] =
reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs))
hout : ¬x ∈ acc
this :
(fun x_1 => decide ((decide ¬x_1 ∈ acc) = true ∧ (decide ¬x_1 ∈ [x]) = true)) = fun x_1 =>
decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x])
h_mem_iff : ∀ (x_1 : α), x_1 ∈ x :: acc ↔ x_1 ∈ [x] ∨ x_1 ∈ acc
h_mem_iff_neg : ∀ (x_1 : α), ¬x_1 ∈ x :: acc ↔ ¬(x_1 ∈ [x] ∨ x_1 ∈ acc)
a : α
⊢ (¬a ∈ x :: acc) = (¬a ∈ acc ∧ ¬a ∈ [x]) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.uniqueAux_acc_append_filter | [1075, 1] | [1134, 25] | apply funext | α : Type u_1
inst✝ : DecidableEq α
x : α
xs acc : List α
hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs)
hterm' : length xs < Nat.succ (length xs)
ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs)
ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs)
ih₃ :
uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] =
reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs))
hout : ¬x ∈ acc
⊢ (fun x_1 => decide ((decide ¬x_1 ∈ acc) = true ∧ (decide ¬x_1 ∈ [x]) = true)) = fun x_1 =>
decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x]) | case h
α : Type u_1
inst✝ : DecidableEq α
x : α
xs acc : List α
hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs)
hterm' : length xs < Nat.succ (length xs)
ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs)
ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs)
ih₃ :
uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] =
reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs))
hout : ¬x ∈ acc
⊢ ∀ (x_1 : α), decide ((decide ¬x_1 ∈ acc) = true ∧ (decide ¬x_1 ∈ [x]) = true) = decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x]) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.uniqueAux_acc_append_filter | [1075, 1] | [1134, 25] | intro x_1 | case h
α : Type u_1
inst✝ : DecidableEq α
x : α
xs acc : List α
hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs)
hterm' : length xs < Nat.succ (length xs)
ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs)
ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs)
ih₃ :
uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] =
reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs))
hout : ¬x ∈ acc
⊢ ∀ (x_1 : α), decide ((decide ¬x_1 ∈ acc) = true ∧ (decide ¬x_1 ∈ [x]) = true) = decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x]) | case h
α : Type u_1
inst✝ : DecidableEq α
x : α
xs acc : List α
hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs)
hterm' : length xs < Nat.succ (length xs)
ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs)
ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_2 => decide ¬x_2 ∈ x :: acc) xs)
ih₃ :
uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] =
reverse [x] ++ unique (filter (fun x_2 => decide ¬x_2 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs))
hout : ¬x ∈ acc
x_1 : α
⊢ decide ((decide ¬x_1 ∈ acc) = true ∧ (decide ¬x_1 ∈ [x]) = true) = decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x]) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.uniqueAux_acc_append_filter | [1075, 1] | [1134, 25] | simp only [decide_not, Bool.not_eq_true'] | case h
α : Type u_1
inst✝ : DecidableEq α
x : α
xs acc : List α
hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs)
hterm' : length xs < Nat.succ (length xs)
ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs)
ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_2 => decide ¬x_2 ∈ x :: acc) xs)
ih₃ :
uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] =
reverse [x] ++ unique (filter (fun x_2 => decide ¬x_2 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs))
hout : ¬x ∈ acc
x_1 : α
⊢ decide ((decide ¬x_1 ∈ acc) = true ∧ (decide ¬x_1 ∈ [x]) = true) = decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x]) | case h
α : Type u_1
inst✝ : DecidableEq α
x : α
xs acc : List α
hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs)
hterm' : length xs < Nat.succ (length xs)
ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs)
ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_2 => decide ¬x_2 ∈ x :: acc) xs)
ih₃ :
uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] =
reverse [x] ++ unique (filter (fun x_2 => decide ¬x_2 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs))
hout : ¬x ∈ acc
x_1 : α
⊢ decide (decide (x_1 ∈ acc) = false ∧ decide (x_1 ∈ [x]) = false) = decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x]) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.uniqueAux_acc_append_filter | [1075, 1] | [1134, 25] | cases Decidable.em (x_1 ∈ acc) with
| inl hmem =>
simp only [hmem, decide_True, not_true_eq_false, false_and]
| inr hnmem =>
simp only [hnmem, decide_False, not_false_eq_true, true_and,
decide_not]
cases Decidable.em (x_1 ∈ [x]) with
| inl hmem' => simp only [hmem', decide_True, decide_False, not]
| inr hnmem' => simp only [hnmem', decide_True, decide_False, not] | case h
α : Type u_1
inst✝ : DecidableEq α
x : α
xs acc : List α
hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs)
hterm' : length xs < Nat.succ (length xs)
ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs)
ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_2 => decide ¬x_2 ∈ x :: acc) xs)
ih₃ :
uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] =
reverse [x] ++ unique (filter (fun x_2 => decide ¬x_2 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs))
hout : ¬x ∈ acc
x_1 : α
⊢ decide (decide (x_1 ∈ acc) = false ∧ decide (x_1 ∈ [x]) = false) = decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x]) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.uniqueAux_acc_append_filter | [1075, 1] | [1134, 25] | simp only [hmem, decide_True, not_true_eq_false, false_and] | case h.inl
α : Type u_1
inst✝ : DecidableEq α
x : α
xs acc : List α
hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs)
hterm' : length xs < Nat.succ (length xs)
ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs)
ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_2 => decide ¬x_2 ∈ x :: acc) xs)
ih₃ :
uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] =
reverse [x] ++ unique (filter (fun x_2 => decide ¬x_2 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs))
hout : ¬x ∈ acc
x_1 : α
hmem : x_1 ∈ acc
⊢ decide (decide (x_1 ∈ acc) = false ∧ decide (x_1 ∈ [x]) = false) = decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x]) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.uniqueAux_acc_append_filter | [1075, 1] | [1134, 25] | simp only [hnmem, decide_False, not_false_eq_true, true_and,
decide_not] | case h.inr
α : Type u_1
inst✝ : DecidableEq α
x : α
xs acc : List α
hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs)
hterm' : length xs < Nat.succ (length xs)
ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs)
ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_2 => decide ¬x_2 ∈ x :: acc) xs)
ih₃ :
uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] =
reverse [x] ++ unique (filter (fun x_2 => decide ¬x_2 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs))
hout : ¬x ∈ acc
x_1 : α
hnmem : ¬x_1 ∈ acc
⊢ decide (decide (x_1 ∈ acc) = false ∧ decide (x_1 ∈ [x]) = false) = decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x]) | case h.inr
α : Type u_1
inst✝ : DecidableEq α
x : α
xs acc : List α
hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs)
hterm' : length xs < Nat.succ (length xs)
ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs)
ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_2 => decide ¬x_2 ∈ x :: acc) xs)
ih₃ :
uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] =
reverse [x] ++ unique (filter (fun x_2 => decide ¬x_2 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs))
hout : ¬x ∈ acc
x_1 : α
hnmem : ¬x_1 ∈ acc
⊢ decide (decide (x_1 ∈ [x]) = false) = !decide (x_1 ∈ [x]) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.uniqueAux_acc_append_filter | [1075, 1] | [1134, 25] | cases Decidable.em (x_1 ∈ [x]) with
| inl hmem' => simp only [hmem', decide_True, decide_False, not]
| inr hnmem' => simp only [hnmem', decide_True, decide_False, not] | case h.inr
α : Type u_1
inst✝ : DecidableEq α
x : α
xs acc : List α
hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs)
hterm' : length xs < Nat.succ (length xs)
ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs)
ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_2 => decide ¬x_2 ∈ x :: acc) xs)
ih₃ :
uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] =
reverse [x] ++ unique (filter (fun x_2 => decide ¬x_2 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs))
hout : ¬x ∈ acc
x_1 : α
hnmem : ¬x_1 ∈ acc
⊢ decide (decide (x_1 ∈ [x]) = false) = !decide (x_1 ∈ [x]) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.uniqueAux_acc_append_filter | [1075, 1] | [1134, 25] | simp only [hmem', decide_True, decide_False, not] | case h.inr.inl
α : Type u_1
inst✝ : DecidableEq α
x : α
xs acc : List α
hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs)
hterm' : length xs < Nat.succ (length xs)
ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs)
ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_2 => decide ¬x_2 ∈ x :: acc) xs)
ih₃ :
uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] =
reverse [x] ++ unique (filter (fun x_2 => decide ¬x_2 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs))
hout : ¬x ∈ acc
x_1 : α
hnmem : ¬x_1 ∈ acc
hmem' : x_1 ∈ [x]
⊢ decide (decide (x_1 ∈ [x]) = false) = !decide (x_1 ∈ [x]) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.uniqueAux_acc_append_filter | [1075, 1] | [1134, 25] | simp only [hnmem', decide_True, decide_False, not] | case h.inr.inr
α : Type u_1
inst✝ : DecidableEq α
x : α
xs acc : List α
hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs)
hterm' : length xs < Nat.succ (length xs)
ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs)
ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_2 => decide ¬x_2 ∈ x :: acc) xs)
ih₃ :
uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] =
reverse [x] ++ unique (filter (fun x_2 => decide ¬x_2 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs))
hout : ¬x ∈ acc
x_1 : α
hnmem : ¬x_1 ∈ acc
hnmem' : ¬x_1 ∈ [x]
⊢ decide (decide (x_1 ∈ [x]) = false) = !decide (x_1 ∈ [x]) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.uniqueAux_acc_append_filter | [1075, 1] | [1134, 25] | assumption | α : Type u_1
inst✝ : DecidableEq α
_x✝ : (_ : List α) ×' List α
a✝¹ :
∀ (y : (_ : List α) ×' List α),
(invImage (fun a => PSigma.casesOn a fun xs snd => length xs) instWellFoundedRelation).1 y _x✝ →
uniqueAux y.1 y.2 = reverse y.2 ++ unique (filter (fun x => decide ¬x ∈ y.2) y.1)
x✝² x✝¹ : List α
a✝ :
∀ (y : (_ : List α) ×' List α),
(invImage (fun a => PSigma.casesOn a fun xs snd => length xs) instWellFoundedRelation).1 y
{ fst := x✝², snd := x✝¹ } →
uniqueAux y.1 y.2 = reverse y.2 ++ unique (filter (fun x => decide ¬x ∈ y.2) y.1)
x : α
xs ys : List α
x✝ :
∀ (y : (_ : List α) ×' List α),
(invImage (fun a => PSigma.casesOn a fun xs snd => length xs) instWellFoundedRelation).1 y
{ fst := x :: xs, snd := ys } →
uniqueAux y.1 y.2 = reverse y.2 ++ unique (filter (fun x => decide ¬x ∈ y.2) y.1)
hterm : length (filter (fun a => decide ¬a ∈ ys) xs) < Nat.succ (length xs)
hterm' : length xs < Nat.succ (length xs)
⊢ (invImage (fun a => PSigma.casesOn a fun xs snd => length xs) instWellFoundedRelation).1 { fst := xs, snd := ys }
{ fst := x :: xs, snd := ys } | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.uniqueAux_acc_append | [1136, 1] | [1155, 14] | have : filter (fun a => decide ¬a ∈ acc) xs = xs := by
induction xs with
| nil => simp [filter]
| cons x xs ih =>
simp only [filter]
have : decide (¬x ∈ acc) = true := by simp [h x (Mem.head _)]
rw [this]
simp only
rw [ih]
. intros x hx
apply h x (Mem.tail _ hx) | α : Type u_1
inst✝ : DecidableEq α
xs acc : List α
h : ∀ (x : α), x ∈ xs → ¬x ∈ acc
⊢ uniqueAux xs acc = reverse acc ++ unique xs | α : Type u_1
inst✝ : DecidableEq α
xs acc : List α
h : ∀ (x : α), x ∈ xs → ¬x ∈ acc
this : filter (fun a => decide ¬a ∈ acc) xs = xs
⊢ uniqueAux xs acc = reverse acc ++ unique xs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.uniqueAux_acc_append | [1136, 1] | [1155, 14] | rw [uniqueAux_acc_append_filter] | α : Type u_1
inst✝ : DecidableEq α
xs acc : List α
h : ∀ (x : α), x ∈ xs → ¬x ∈ acc
this : filter (fun a => decide ¬a ∈ acc) xs = xs
⊢ uniqueAux xs acc = reverse acc ++ unique xs | α : Type u_1
inst✝ : DecidableEq α
xs acc : List α
h : ∀ (x : α), x ∈ xs → ¬x ∈ acc
this : filter (fun a => decide ¬a ∈ acc) xs = xs
⊢ reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) = reverse acc ++ unique xs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.uniqueAux_acc_append | [1136, 1] | [1155, 14] | cases xs with
| nil => apply congrArg; simp [filter]
| cons x xs =>
apply congrArg
rw [this] | α : Type u_1
inst✝ : DecidableEq α
xs acc : List α
h : ∀ (x : α), x ∈ xs → ¬x ∈ acc
this : filter (fun a => decide ¬a ∈ acc) xs = xs
⊢ reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) = reverse acc ++ unique xs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.uniqueAux_acc_append | [1136, 1] | [1155, 14] | induction xs with
| nil => simp [filter]
| cons x xs ih =>
simp only [filter]
have : decide (¬x ∈ acc) = true := by simp [h x (Mem.head _)]
rw [this]
simp only
rw [ih]
. intros x hx
apply h x (Mem.tail _ hx) | α : Type u_1
inst✝ : DecidableEq α
xs acc : List α
h : ∀ (x : α), x ∈ xs → ¬x ∈ acc
⊢ filter (fun a => decide ¬a ∈ acc) xs = xs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.uniqueAux_acc_append | [1136, 1] | [1155, 14] | simp [filter] | case nil
α : Type u_1
inst✝ : DecidableEq α
acc : List α
h : ∀ (x : α), x ∈ [] → ¬x ∈ acc
⊢ filter (fun a => decide ¬a ∈ acc) [] = [] | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.uniqueAux_acc_append | [1136, 1] | [1155, 14] | simp only [filter] | case cons
α : Type u_1
inst✝ : DecidableEq α
acc : List α
x : α
xs : List α
ih : (∀ (x : α), x ∈ xs → ¬x ∈ acc) → filter (fun a => decide ¬a ∈ acc) xs = xs
h : ∀ (x_1 : α), x_1 ∈ x :: xs → ¬x_1 ∈ acc
⊢ filter (fun a => decide ¬a ∈ acc) (x :: xs) = x :: xs | case cons
α : Type u_1
inst✝ : DecidableEq α
acc : List α
x : α
xs : List α
ih : (∀ (x : α), x ∈ xs → ¬x ∈ acc) → filter (fun a => decide ¬a ∈ acc) xs = xs
h : ∀ (x_1 : α), x_1 ∈ x :: xs → ¬x_1 ∈ acc
⊢ (match decide ¬x ∈ acc with
| true => x :: filter (fun a => decide ¬a ∈ acc) xs
| false => filter (fun a => decide ¬a ∈ acc) xs) =
x :: xs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.uniqueAux_acc_append | [1136, 1] | [1155, 14] | have : decide (¬x ∈ acc) = true := by simp [h x (Mem.head _)] | case cons
α : Type u_1
inst✝ : DecidableEq α
acc : List α
x : α
xs : List α
ih : (∀ (x : α), x ∈ xs → ¬x ∈ acc) → filter (fun a => decide ¬a ∈ acc) xs = xs
h : ∀ (x_1 : α), x_1 ∈ x :: xs → ¬x_1 ∈ acc
⊢ (match decide ¬x ∈ acc with
| true => x :: filter (fun a => decide ¬a ∈ acc) xs
| false => filter (fun a => decide ¬a ∈ acc) xs) =
x :: xs | case cons
α : Type u_1
inst✝ : DecidableEq α
acc : List α
x : α
xs : List α
ih : (∀ (x : α), x ∈ xs → ¬x ∈ acc) → filter (fun a => decide ¬a ∈ acc) xs = xs
h : ∀ (x_1 : α), x_1 ∈ x :: xs → ¬x_1 ∈ acc
this : (decide ¬x ∈ acc) = true
⊢ (match decide ¬x ∈ acc with
| true => x :: filter (fun a => decide ¬a ∈ acc) xs
| false => filter (fun a => decide ¬a ∈ acc) xs) =
x :: xs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.uniqueAux_acc_append | [1136, 1] | [1155, 14] | rw [this] | case cons
α : Type u_1
inst✝ : DecidableEq α
acc : List α
x : α
xs : List α
ih : (∀ (x : α), x ∈ xs → ¬x ∈ acc) → filter (fun a => decide ¬a ∈ acc) xs = xs
h : ∀ (x_1 : α), x_1 ∈ x :: xs → ¬x_1 ∈ acc
this : (decide ¬x ∈ acc) = true
⊢ (match decide ¬x ∈ acc with
| true => x :: filter (fun a => decide ¬a ∈ acc) xs
| false => filter (fun a => decide ¬a ∈ acc) xs) =
x :: xs | case cons
α : Type u_1
inst✝ : DecidableEq α
acc : List α
x : α
xs : List α
ih : (∀ (x : α), x ∈ xs → ¬x ∈ acc) → filter (fun a => decide ¬a ∈ acc) xs = xs
h : ∀ (x_1 : α), x_1 ∈ x :: xs → ¬x_1 ∈ acc
this : (decide ¬x ∈ acc) = true
⊢ (match true with
| true => x :: filter (fun a => decide ¬a ∈ acc) xs
| false => filter (fun a => decide ¬a ∈ acc) xs) =
x :: xs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.uniqueAux_acc_append | [1136, 1] | [1155, 14] | simp only | case cons
α : Type u_1
inst✝ : DecidableEq α
acc : List α
x : α
xs : List α
ih : (∀ (x : α), x ∈ xs → ¬x ∈ acc) → filter (fun a => decide ¬a ∈ acc) xs = xs
h : ∀ (x_1 : α), x_1 ∈ x :: xs → ¬x_1 ∈ acc
this : (decide ¬x ∈ acc) = true
⊢ (match true with
| true => x :: filter (fun a => decide ¬a ∈ acc) xs
| false => filter (fun a => decide ¬a ∈ acc) xs) =
x :: xs | case cons
α : Type u_1
inst✝ : DecidableEq α
acc : List α
x : α
xs : List α
ih : (∀ (x : α), x ∈ xs → ¬x ∈ acc) → filter (fun a => decide ¬a ∈ acc) xs = xs
h : ∀ (x_1 : α), x_1 ∈ x :: xs → ¬x_1 ∈ acc
this : (decide ¬x ∈ acc) = true
⊢ x :: filter (fun a => decide ¬a ∈ acc) xs = x :: xs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.uniqueAux_acc_append | [1136, 1] | [1155, 14] | rw [ih] | case cons
α : Type u_1
inst✝ : DecidableEq α
acc : List α
x : α
xs : List α
ih : (∀ (x : α), x ∈ xs → ¬x ∈ acc) → filter (fun a => decide ¬a ∈ acc) xs = xs
h : ∀ (x_1 : α), x_1 ∈ x :: xs → ¬x_1 ∈ acc
this : (decide ¬x ∈ acc) = true
⊢ x :: filter (fun a => decide ¬a ∈ acc) xs = x :: xs | case cons
α : Type u_1
inst✝ : DecidableEq α
acc : List α
x : α
xs : List α
ih : (∀ (x : α), x ∈ xs → ¬x ∈ acc) → filter (fun a => decide ¬a ∈ acc) xs = xs
h : ∀ (x_1 : α), x_1 ∈ x :: xs → ¬x_1 ∈ acc
this : (decide ¬x ∈ acc) = true
⊢ ∀ (x : α), x ∈ xs → ¬x ∈ acc |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.uniqueAux_acc_append | [1136, 1] | [1155, 14] | . intros x hx
apply h x (Mem.tail _ hx) | case cons
α : Type u_1
inst✝ : DecidableEq α
acc : List α
x : α
xs : List α
ih : (∀ (x : α), x ∈ xs → ¬x ∈ acc) → filter (fun a => decide ¬a ∈ acc) xs = xs
h : ∀ (x_1 : α), x_1 ∈ x :: xs → ¬x_1 ∈ acc
this : (decide ¬x ∈ acc) = true
⊢ ∀ (x : α), x ∈ xs → ¬x ∈ acc | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.uniqueAux_acc_append | [1136, 1] | [1155, 14] | simp [h x (Mem.head _)] | α : Type u_1
inst✝ : DecidableEq α
acc : List α
x : α
xs : List α
ih : (∀ (x : α), x ∈ xs → ¬x ∈ acc) → filter (fun a => decide ¬a ∈ acc) xs = xs
h : ∀ (x_1 : α), x_1 ∈ x :: xs → ¬x_1 ∈ acc
⊢ (decide ¬x ∈ acc) = true | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.uniqueAux_acc_append | [1136, 1] | [1155, 14] | intros x hx | case cons
α : Type u_1
inst✝ : DecidableEq α
acc : List α
x : α
xs : List α
ih : (∀ (x : α), x ∈ xs → ¬x ∈ acc) → filter (fun a => decide ¬a ∈ acc) xs = xs
h : ∀ (x_1 : α), x_1 ∈ x :: xs → ¬x_1 ∈ acc
this : (decide ¬x ∈ acc) = true
⊢ ∀ (x : α), x ∈ xs → ¬x ∈ acc | case cons
α : Type u_1
inst✝ : DecidableEq α
acc : List α
x✝ : α
xs : List α
ih : (∀ (x : α), x ∈ xs → ¬x ∈ acc) → filter (fun a => decide ¬a ∈ acc) xs = xs
h : ∀ (x : α), x ∈ x✝ :: xs → ¬x ∈ acc
this : (decide ¬x✝ ∈ acc) = true
x : α
hx : x ∈ xs
⊢ ¬x ∈ acc |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.uniqueAux_acc_append | [1136, 1] | [1155, 14] | apply h x (Mem.tail _ hx) | case cons
α : Type u_1
inst✝ : DecidableEq α
acc : List α
x✝ : α
xs : List α
ih : (∀ (x : α), x ∈ xs → ¬x ∈ acc) → filter (fun a => decide ¬a ∈ acc) xs = xs
h : ∀ (x : α), x ∈ x✝ :: xs → ¬x ∈ acc
this : (decide ¬x✝ ∈ acc) = true
x : α
hx : x ∈ xs
⊢ ¬x ∈ acc | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.uniqueAux_acc_append | [1136, 1] | [1155, 14] | apply congrArg | case nil
α : Type u_1
inst✝ : DecidableEq α
acc : List α
h : ∀ (x : α), x ∈ [] → ¬x ∈ acc
this : filter (fun a => decide ¬a ∈ acc) [] = []
⊢ reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) []) = reverse acc ++ unique [] | case nil.h
α : Type u_1
inst✝ : DecidableEq α
acc : List α
h : ∀ (x : α), x ∈ [] → ¬x ∈ acc
this : filter (fun a => decide ¬a ∈ acc) [] = []
⊢ unique (filter (fun x => decide ¬x ∈ acc) []) = unique [] |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.uniqueAux_acc_append | [1136, 1] | [1155, 14] | simp [filter] | case nil.h
α : Type u_1
inst✝ : DecidableEq α
acc : List α
h : ∀ (x : α), x ∈ [] → ¬x ∈ acc
this : filter (fun a => decide ¬a ∈ acc) [] = []
⊢ unique (filter (fun x => decide ¬x ∈ acc) []) = unique [] | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.uniqueAux_acc_append | [1136, 1] | [1155, 14] | apply congrArg | case cons
α : Type u_1
inst✝ : DecidableEq α
acc : List α
x : α
xs : List α
h : ∀ (x_1 : α), x_1 ∈ x :: xs → ¬x_1 ∈ acc
this : filter (fun a => decide ¬a ∈ acc) (x :: xs) = x :: xs
⊢ reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) (x :: xs)) = reverse acc ++ unique (x :: xs) | case cons.h
α : Type u_1
inst✝ : DecidableEq α
acc : List α
x : α
xs : List α
h : ∀ (x_1 : α), x_1 ∈ x :: xs → ¬x_1 ∈ acc
this : filter (fun a => decide ¬a ∈ acc) (x :: xs) = x :: xs
⊢ unique (filter (fun x => decide ¬x ∈ acc) (x :: xs)) = unique (x :: xs) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.uniqueAux_acc_append | [1136, 1] | [1155, 14] | rw [this] | case cons.h
α : Type u_1
inst✝ : DecidableEq α
acc : List α
x : α
xs : List α
h : ∀ (x_1 : α), x_1 ∈ x :: xs → ¬x_1 ∈ acc
this : filter (fun a => decide ¬a ∈ acc) (x :: xs) = x :: xs
⊢ unique (filter (fun x => decide ¬x ∈ acc) (x :: xs)) = unique (x :: xs) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux | [1157, 1] | [1160, 79] | rw [uniqueAux_acc_append _ _ h, length_append, length_reverse, Nat.add_comm] | α : Type u_1
inst✝ : DecidableEq α
xs acc : List α
h : ∀ (x : α), x ∈ xs → ¬x ∈ acc
⊢ length (uniqueAux xs acc) = length (unique xs) + length acc | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.matchKey_fst_eq_filter_k_map_snd | [1212, 1] | [1225, 47] | intros xs k | κ : Type u_1
ν : Type u_2
inst : DecidableEq κ
⊢ ∀ (xs : List (κ × ν)) (k : κ), (matchKey xs k).fst = map Prod.snd (filter (fun x => decide (x.fst = k)) xs) | κ : Type u_1
ν : Type u_2
inst : DecidableEq κ
xs : List (κ × ν)
k : κ
⊢ (matchKey xs k).fst = map Prod.snd (filter (fun x => decide (x.fst = k)) xs) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.matchKey_fst_eq_filter_k_map_snd | [1212, 1] | [1225, 47] | induction xs with
| nil => rfl
| cons x xs ih =>
simp only [matchKey]
cases inst x.1 k with
| isFalse hfalse =>
simp only [hfalse, ite_false, ih, filter]
exact rfl
| isTrue htrue =>
simp [htrue, ite_true, filter, ih, map] | κ : Type u_1
ν : Type u_2
inst : DecidableEq κ
xs : List (κ × ν)
k : κ
⊢ (matchKey xs k).fst = map Prod.snd (filter (fun x => decide (x.fst = k)) xs) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.matchKey_fst_eq_filter_k_map_snd | [1212, 1] | [1225, 47] | rfl | case nil
κ : Type u_1
ν : Type u_2
inst : DecidableEq κ
k : κ
⊢ (matchKey [] k).fst = map Prod.snd (filter (fun x => decide (x.fst = k)) []) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.matchKey_fst_eq_filter_k_map_snd | [1212, 1] | [1225, 47] | simp only [matchKey] | case cons
κ : Type u_1
ν : Type u_2
inst : DecidableEq κ
k : κ
x : κ × ν
xs : List (κ × ν)
ih : (matchKey xs k).fst = map Prod.snd (filter (fun x => decide (x.fst = k)) xs)
⊢ (matchKey (x :: xs) k).fst = map Prod.snd (filter (fun x => decide (x.fst = k)) (x :: xs)) | case cons
κ : Type u_1
ν : Type u_2
inst : DecidableEq κ
k : κ
x : κ × ν
xs : List (κ × ν)
ih : (matchKey xs k).fst = map Prod.snd (filter (fun x => decide (x.fst = k)) xs)
⊢ (if x.fst = k then (x.snd :: (matchKey xs k).fst, (matchKey xs k).snd)
else ((matchKey xs k).fst, (x.fst, x.snd) :: (matchKey xs k).snd)).fst =
map Prod.snd (filter (fun x => decide (x.fst = k)) (x :: xs)) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.matchKey_fst_eq_filter_k_map_snd | [1212, 1] | [1225, 47] | cases inst x.1 k with
| isFalse hfalse =>
simp only [hfalse, ite_false, ih, filter]
exact rfl
| isTrue htrue =>
simp [htrue, ite_true, filter, ih, map] | case cons
κ : Type u_1
ν : Type u_2
inst : DecidableEq κ
k : κ
x : κ × ν
xs : List (κ × ν)
ih : (matchKey xs k).fst = map Prod.snd (filter (fun x => decide (x.fst = k)) xs)
⊢ (if x.fst = k then (x.snd :: (matchKey xs k).fst, (matchKey xs k).snd)
else ((matchKey xs k).fst, (x.fst, x.snd) :: (matchKey xs k).snd)).fst =
map Prod.snd (filter (fun x => decide (x.fst = k)) (x :: xs)) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.matchKey_fst_eq_filter_k_map_snd | [1212, 1] | [1225, 47] | simp only [hfalse, ite_false, ih, filter] | case cons.isFalse
κ : Type u_1
ν : Type u_2
inst : DecidableEq κ
k : κ
x : κ × ν
xs : List (κ × ν)
ih : (matchKey xs k).fst = map Prod.snd (filter (fun x => decide (x.fst = k)) xs)
hfalse : ¬x.fst = k
⊢ (if x.fst = k then (x.snd :: (matchKey xs k).fst, (matchKey xs k).snd)
else ((matchKey xs k).fst, (x.fst, x.snd) :: (matchKey xs k).snd)).fst =
map Prod.snd (filter (fun x => decide (x.fst = k)) (x :: xs)) | case cons.isFalse
κ : Type u_1
ν : Type u_2
inst : DecidableEq κ
k : κ
x : κ × ν
xs : List (κ × ν)
ih : (matchKey xs k).fst = map Prod.snd (filter (fun x => decide (x.fst = k)) xs)
hfalse : ¬x.fst = k
⊢ map Prod.snd (filter (fun x => decide (x.fst = k)) xs) =
map Prod.snd
(match decide False with
| true => x :: filter (fun x => decide (x.fst = k)) xs
| false => filter (fun x => decide (x.fst = k)) xs) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.matchKey_fst_eq_filter_k_map_snd | [1212, 1] | [1225, 47] | exact rfl | case cons.isFalse
κ : Type u_1
ν : Type u_2
inst : DecidableEq κ
k : κ
x : κ × ν
xs : List (κ × ν)
ih : (matchKey xs k).fst = map Prod.snd (filter (fun x => decide (x.fst = k)) xs)
hfalse : ¬x.fst = k
⊢ map Prod.snd (filter (fun x => decide (x.fst = k)) xs) =
map Prod.snd
(match decide False with
| true => x :: filter (fun x => decide (x.fst = k)) xs
| false => filter (fun x => decide (x.fst = k)) xs) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.matchKey_fst_eq_filter_k_map_snd | [1212, 1] | [1225, 47] | simp [htrue, ite_true, filter, ih, map] | case cons.isTrue
κ : Type u_1
ν : Type u_2
inst : DecidableEq κ
k : κ
x : κ × ν
xs : List (κ × ν)
ih : (matchKey xs k).fst = map Prod.snd (filter (fun x => decide (x.fst = k)) xs)
htrue : x.fst = k
⊢ (if x.fst = k then (x.snd :: (matchKey xs k).fst, (matchKey xs k).snd)
else ((matchKey xs k).fst, (x.fst, x.snd) :: (matchKey xs k).snd)).fst =
map Prod.snd (filter (fun x => decide (x.fst = k)) (x :: xs)) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.groupByKey_matchKey_snd_length_cons | [1243, 1] | [1254, 48] | simp only [matchKey, length, ite_true] | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
v : ν
xs : List (κ × ν)
⊢ 1 + length (groupByKey (matchKey ((k, v) :: xs) k).snd) = 1 + length (groupByKey (matchKey xs k).snd) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_matchKey | [1256, 1] | [1282, 54] | induction xs with
| nil => intros; simp [uniqueAux]
| cons x xs ih =>
intros acc hk
simp only [length, uniqueAux]
cases Decidable.em (x.fst ∈ acc) with
| inl hin =>
simp only [hin, ite_true, matchKey]
rw [ih _ hk]
cases Decidable.em (x.1 = k) with
| inl heq => simp only [heq, ite_true]
| inr hneq => simp only [hneq, ite_false, map, uniqueAux, hin, ite_true]
| inr hout =>
simp only [hout, ite_false, matchKey]
cases Decidable.em (x.1 = k) with
| inl heq =>
apply absurd hk
rw [heq] at hout
exact hout
| inr hneq =>
rw [ih _ (List.Mem.tail _ hk)]
simp only [hneq, ite_false, uniqueAux, hout] | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
xs : List (κ × ν)
k : κ
⊢ ∀ (acc : List κ),
k ∈ acc → length (uniqueAux (map Prod.fst xs) acc) = length (uniqueAux (map Prod.fst (matchKey xs k).snd) acc) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_matchKey | [1256, 1] | [1282, 54] | intros | case nil
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
⊢ ∀ (acc : List κ),
k ∈ acc → length (uniqueAux (map Prod.fst []) acc) = length (uniqueAux (map Prod.fst (matchKey [] k).snd) acc) | case nil
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
acc✝ : List κ
hk✝ : k ∈ acc✝
⊢ length (uniqueAux (map Prod.fst []) acc✝) = length (uniqueAux (map Prod.fst (matchKey [] k).snd) acc✝) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_matchKey | [1256, 1] | [1282, 54] | simp [uniqueAux] | case nil
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
acc✝ : List κ
hk✝ : k ∈ acc✝
⊢ length (uniqueAux (map Prod.fst []) acc✝) = length (uniqueAux (map Prod.fst (matchKey [] k).snd) acc✝) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_matchKey | [1256, 1] | [1282, 54] | intros acc hk | case cons
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
x : κ × ν
xs : List (κ × ν)
ih :
∀ (acc : List κ),
k ∈ acc → length (uniqueAux (map Prod.fst xs) acc) = length (uniqueAux (map Prod.fst (matchKey xs k).snd) acc)
⊢ ∀ (acc : List κ),
k ∈ acc →
length (uniqueAux (map Prod.fst (x :: xs)) acc) = length (uniqueAux (map Prod.fst (matchKey (x :: xs) k).snd) acc) | case cons
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
x : κ × ν
xs : List (κ × ν)
ih :
∀ (acc : List κ),
k ∈ acc → length (uniqueAux (map Prod.fst xs) acc) = length (uniqueAux (map Prod.fst (matchKey xs k).snd) acc)
acc : List κ
hk : k ∈ acc
⊢ length (uniqueAux (map Prod.fst (x :: xs)) acc) = length (uniqueAux (map Prod.fst (matchKey (x :: xs) k).snd) acc) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_matchKey | [1256, 1] | [1282, 54] | simp only [length, uniqueAux] | case cons
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
x : κ × ν
xs : List (κ × ν)
ih :
∀ (acc : List κ),
k ∈ acc → length (uniqueAux (map Prod.fst xs) acc) = length (uniqueAux (map Prod.fst (matchKey xs k).snd) acc)
acc : List κ
hk : k ∈ acc
⊢ length (uniqueAux (map Prod.fst (x :: xs)) acc) = length (uniqueAux (map Prod.fst (matchKey (x :: xs) k).snd) acc) | case cons
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
x : κ × ν
xs : List (κ × ν)
ih :
∀ (acc : List κ),
k ∈ acc → length (uniqueAux (map Prod.fst xs) acc) = length (uniqueAux (map Prod.fst (matchKey xs k).snd) acc)
acc : List κ
hk : k ∈ acc
⊢ length (if x.fst ∈ acc then uniqueAux (map Prod.fst xs) acc else uniqueAux (map Prod.fst xs) (x.fst :: acc)) =
length (uniqueAux (map Prod.fst (matchKey (x :: xs) k).snd) acc) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_matchKey | [1256, 1] | [1282, 54] | cases Decidable.em (x.fst ∈ acc) with
| inl hin =>
simp only [hin, ite_true, matchKey]
rw [ih _ hk]
cases Decidable.em (x.1 = k) with
| inl heq => simp only [heq, ite_true]
| inr hneq => simp only [hneq, ite_false, map, uniqueAux, hin, ite_true]
| inr hout =>
simp only [hout, ite_false, matchKey]
cases Decidable.em (x.1 = k) with
| inl heq =>
apply absurd hk
rw [heq] at hout
exact hout
| inr hneq =>
rw [ih _ (List.Mem.tail _ hk)]
simp only [hneq, ite_false, uniqueAux, hout] | case cons
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
x : κ × ν
xs : List (κ × ν)
ih :
∀ (acc : List κ),
k ∈ acc → length (uniqueAux (map Prod.fst xs) acc) = length (uniqueAux (map Prod.fst (matchKey xs k).snd) acc)
acc : List κ
hk : k ∈ acc
⊢ length (if x.fst ∈ acc then uniqueAux (map Prod.fst xs) acc else uniqueAux (map Prod.fst xs) (x.fst :: acc)) =
length (uniqueAux (map Prod.fst (matchKey (x :: xs) k).snd) acc) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_matchKey | [1256, 1] | [1282, 54] | simp only [hin, ite_true, matchKey] | case cons.inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
x : κ × ν
xs : List (κ × ν)
ih :
∀ (acc : List κ),
k ∈ acc → length (uniqueAux (map Prod.fst xs) acc) = length (uniqueAux (map Prod.fst (matchKey xs k).snd) acc)
acc : List κ
hk : k ∈ acc
hin : x.fst ∈ acc
⊢ length (if x.fst ∈ acc then uniqueAux (map Prod.fst xs) acc else uniqueAux (map Prod.fst xs) (x.fst :: acc)) =
length (uniqueAux (map Prod.fst (matchKey (x :: xs) k).snd) acc) | case cons.inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
x : κ × ν
xs : List (κ × ν)
ih :
∀ (acc : List κ),
k ∈ acc → length (uniqueAux (map Prod.fst xs) acc) = length (uniqueAux (map Prod.fst (matchKey xs k).snd) acc)
acc : List κ
hk : k ∈ acc
hin : x.fst ∈ acc
⊢ length (uniqueAux (map Prod.fst xs) acc) =
length
(uniqueAux
(map Prod.fst
(if x.fst = k then (x.snd :: (matchKey xs k).fst, (matchKey xs k).snd)
else ((matchKey xs k).fst, (x.fst, x.snd) :: (matchKey xs k).snd)).snd)
acc) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_matchKey | [1256, 1] | [1282, 54] | rw [ih _ hk] | case cons.inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
x : κ × ν
xs : List (κ × ν)
ih :
∀ (acc : List κ),
k ∈ acc → length (uniqueAux (map Prod.fst xs) acc) = length (uniqueAux (map Prod.fst (matchKey xs k).snd) acc)
acc : List κ
hk : k ∈ acc
hin : x.fst ∈ acc
⊢ length (uniqueAux (map Prod.fst xs) acc) =
length
(uniqueAux
(map Prod.fst
(if x.fst = k then (x.snd :: (matchKey xs k).fst, (matchKey xs k).snd)
else ((matchKey xs k).fst, (x.fst, x.snd) :: (matchKey xs k).snd)).snd)
acc) | case cons.inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
x : κ × ν
xs : List (κ × ν)
ih :
∀ (acc : List κ),
k ∈ acc → length (uniqueAux (map Prod.fst xs) acc) = length (uniqueAux (map Prod.fst (matchKey xs k).snd) acc)
acc : List κ
hk : k ∈ acc
hin : x.fst ∈ acc
⊢ length (uniqueAux (map Prod.fst (matchKey xs k).snd) acc) =
length
(uniqueAux
(map Prod.fst
(if x.fst = k then (x.snd :: (matchKey xs k).fst, (matchKey xs k).snd)
else ((matchKey xs k).fst, (x.fst, x.snd) :: (matchKey xs k).snd)).snd)
acc) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_matchKey | [1256, 1] | [1282, 54] | cases Decidable.em (x.1 = k) with
| inl heq => simp only [heq, ite_true]
| inr hneq => simp only [hneq, ite_false, map, uniqueAux, hin, ite_true] | case cons.inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
x : κ × ν
xs : List (κ × ν)
ih :
∀ (acc : List κ),
k ∈ acc → length (uniqueAux (map Prod.fst xs) acc) = length (uniqueAux (map Prod.fst (matchKey xs k).snd) acc)
acc : List κ
hk : k ∈ acc
hin : x.fst ∈ acc
⊢ length (uniqueAux (map Prod.fst (matchKey xs k).snd) acc) =
length
(uniqueAux
(map Prod.fst
(if x.fst = k then (x.snd :: (matchKey xs k).fst, (matchKey xs k).snd)
else ((matchKey xs k).fst, (x.fst, x.snd) :: (matchKey xs k).snd)).snd)
acc) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_matchKey | [1256, 1] | [1282, 54] | simp only [heq, ite_true] | case cons.inl.inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
x : κ × ν
xs : List (κ × ν)
ih :
∀ (acc : List κ),
k ∈ acc → length (uniqueAux (map Prod.fst xs) acc) = length (uniqueAux (map Prod.fst (matchKey xs k).snd) acc)
acc : List κ
hk : k ∈ acc
hin : x.fst ∈ acc
heq : x.fst = k
⊢ length (uniqueAux (map Prod.fst (matchKey xs k).snd) acc) =
length
(uniqueAux
(map Prod.fst
(if x.fst = k then (x.snd :: (matchKey xs k).fst, (matchKey xs k).snd)
else ((matchKey xs k).fst, (x.fst, x.snd) :: (matchKey xs k).snd)).snd)
acc) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_matchKey | [1256, 1] | [1282, 54] | simp only [hneq, ite_false, map, uniqueAux, hin, ite_true] | case cons.inl.inr
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
x : κ × ν
xs : List (κ × ν)
ih :
∀ (acc : List κ),
k ∈ acc → length (uniqueAux (map Prod.fst xs) acc) = length (uniqueAux (map Prod.fst (matchKey xs k).snd) acc)
acc : List κ
hk : k ∈ acc
hin : x.fst ∈ acc
hneq : ¬x.fst = k
⊢ length (uniqueAux (map Prod.fst (matchKey xs k).snd) acc) =
length
(uniqueAux
(map Prod.fst
(if x.fst = k then (x.snd :: (matchKey xs k).fst, (matchKey xs k).snd)
else ((matchKey xs k).fst, (x.fst, x.snd) :: (matchKey xs k).snd)).snd)
acc) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_matchKey | [1256, 1] | [1282, 54] | simp only [hout, ite_false, matchKey] | case cons.inr
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
x : κ × ν
xs : List (κ × ν)
ih :
∀ (acc : List κ),
k ∈ acc → length (uniqueAux (map Prod.fst xs) acc) = length (uniqueAux (map Prod.fst (matchKey xs k).snd) acc)
acc : List κ
hk : k ∈ acc
hout : ¬x.fst ∈ acc
⊢ length (if x.fst ∈ acc then uniqueAux (map Prod.fst xs) acc else uniqueAux (map Prod.fst xs) (x.fst :: acc)) =
length (uniqueAux (map Prod.fst (matchKey (x :: xs) k).snd) acc) | case cons.inr
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
x : κ × ν
xs : List (κ × ν)
ih :
∀ (acc : List κ),
k ∈ acc → length (uniqueAux (map Prod.fst xs) acc) = length (uniqueAux (map Prod.fst (matchKey xs k).snd) acc)
acc : List κ
hk : k ∈ acc
hout : ¬x.fst ∈ acc
⊢ length (uniqueAux (map Prod.fst xs) (x.fst :: acc)) =
length
(uniqueAux
(map Prod.fst
(if x.fst = k then (x.snd :: (matchKey xs k).fst, (matchKey xs k).snd)
else ((matchKey xs k).fst, (x.fst, x.snd) :: (matchKey xs k).snd)).snd)
acc) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_matchKey | [1256, 1] | [1282, 54] | cases Decidable.em (x.1 = k) with
| inl heq =>
apply absurd hk
rw [heq] at hout
exact hout
| inr hneq =>
rw [ih _ (List.Mem.tail _ hk)]
simp only [hneq, ite_false, uniqueAux, hout] | case cons.inr
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
x : κ × ν
xs : List (κ × ν)
ih :
∀ (acc : List κ),
k ∈ acc → length (uniqueAux (map Prod.fst xs) acc) = length (uniqueAux (map Prod.fst (matchKey xs k).snd) acc)
acc : List κ
hk : k ∈ acc
hout : ¬x.fst ∈ acc
⊢ length (uniqueAux (map Prod.fst xs) (x.fst :: acc)) =
length
(uniqueAux
(map Prod.fst
(if x.fst = k then (x.snd :: (matchKey xs k).fst, (matchKey xs k).snd)
else ((matchKey xs k).fst, (x.fst, x.snd) :: (matchKey xs k).snd)).snd)
acc) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_matchKey | [1256, 1] | [1282, 54] | apply absurd hk | case cons.inr.inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
x : κ × ν
xs : List (κ × ν)
ih :
∀ (acc : List κ),
k ∈ acc → length (uniqueAux (map Prod.fst xs) acc) = length (uniqueAux (map Prod.fst (matchKey xs k).snd) acc)
acc : List κ
hk : k ∈ acc
hout : ¬x.fst ∈ acc
heq : x.fst = k
⊢ length (uniqueAux (map Prod.fst xs) (x.fst :: acc)) =
length
(uniqueAux
(map Prod.fst
(if x.fst = k then (x.snd :: (matchKey xs k).fst, (matchKey xs k).snd)
else ((matchKey xs k).fst, (x.fst, x.snd) :: (matchKey xs k).snd)).snd)
acc) | case cons.inr.inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
x : κ × ν
xs : List (κ × ν)
ih :
∀ (acc : List κ),
k ∈ acc → length (uniqueAux (map Prod.fst xs) acc) = length (uniqueAux (map Prod.fst (matchKey xs k).snd) acc)
acc : List κ
hk : k ∈ acc
hout : ¬x.fst ∈ acc
heq : x.fst = k
⊢ ¬k ∈ acc |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_matchKey | [1256, 1] | [1282, 54] | rw [heq] at hout | case cons.inr.inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
x : κ × ν
xs : List (κ × ν)
ih :
∀ (acc : List κ),
k ∈ acc → length (uniqueAux (map Prod.fst xs) acc) = length (uniqueAux (map Prod.fst (matchKey xs k).snd) acc)
acc : List κ
hk : k ∈ acc
hout : ¬x.fst ∈ acc
heq : x.fst = k
⊢ ¬k ∈ acc | case cons.inr.inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
x : κ × ν
xs : List (κ × ν)
ih :
∀ (acc : List κ),
k ∈ acc → length (uniqueAux (map Prod.fst xs) acc) = length (uniqueAux (map Prod.fst (matchKey xs k).snd) acc)
acc : List κ
hk : k ∈ acc
hout : ¬k ∈ acc
heq : x.fst = k
⊢ ¬k ∈ acc |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_matchKey | [1256, 1] | [1282, 54] | exact hout | case cons.inr.inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
x : κ × ν
xs : List (κ × ν)
ih :
∀ (acc : List κ),
k ∈ acc → length (uniqueAux (map Prod.fst xs) acc) = length (uniqueAux (map Prod.fst (matchKey xs k).snd) acc)
acc : List κ
hk : k ∈ acc
hout : ¬k ∈ acc
heq : x.fst = k
⊢ ¬k ∈ acc | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_matchKey | [1256, 1] | [1282, 54] | rw [ih _ (List.Mem.tail _ hk)] | case cons.inr.inr
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
x : κ × ν
xs : List (κ × ν)
ih :
∀ (acc : List κ),
k ∈ acc → length (uniqueAux (map Prod.fst xs) acc) = length (uniqueAux (map Prod.fst (matchKey xs k).snd) acc)
acc : List κ
hk : k ∈ acc
hout : ¬x.fst ∈ acc
hneq : ¬x.fst = k
⊢ length (uniqueAux (map Prod.fst xs) (x.fst :: acc)) =
length
(uniqueAux
(map Prod.fst
(if x.fst = k then (x.snd :: (matchKey xs k).fst, (matchKey xs k).snd)
else ((matchKey xs k).fst, (x.fst, x.snd) :: (matchKey xs k).snd)).snd)
acc) | case cons.inr.inr
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
x : κ × ν
xs : List (κ × ν)
ih :
∀ (acc : List κ),
k ∈ acc → length (uniqueAux (map Prod.fst xs) acc) = length (uniqueAux (map Prod.fst (matchKey xs k).snd) acc)
acc : List κ
hk : k ∈ acc
hout : ¬x.fst ∈ acc
hneq : ¬x.fst = k
⊢ length (uniqueAux (map Prod.fst (matchKey xs k).snd) (x.fst :: acc)) =
length
(uniqueAux
(map Prod.fst
(if x.fst = k then (x.snd :: (matchKey xs k).fst, (matchKey xs k).snd)
else ((matchKey xs k).fst, (x.fst, x.snd) :: (matchKey xs k).snd)).snd)
acc) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_matchKey | [1256, 1] | [1282, 54] | simp only [hneq, ite_false, uniqueAux, hout] | case cons.inr.inr
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
x : κ × ν
xs : List (κ × ν)
ih :
∀ (acc : List κ),
k ∈ acc → length (uniqueAux (map Prod.fst xs) acc) = length (uniqueAux (map Prod.fst (matchKey xs k).snd) acc)
acc : List κ
hk : k ∈ acc
hout : ¬x.fst ∈ acc
hneq : ¬x.fst = k
⊢ length (uniqueAux (map Prod.fst (matchKey xs k).snd) (x.fst :: acc)) =
length
(uniqueAux
(map Prod.fst
(if x.fst = k then (x.snd :: (matchKey xs k).fst, (matchKey xs k).snd)
else ((matchKey xs k).fst, (x.fst, x.snd) :: (matchKey xs k).snd)).snd)
acc) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_groupByKey | [1294, 1] | [1316, 25] | have hterm : length (matchKey xs k).snd < Nat.succ (length xs) :=
Nat.lt_of_succ_le $ Nat.succ_le_succ $ matchKey_snd_length xs k | κ : Type u_1
inst✝ : DecidableEq κ
ν : Type u_2
k : κ
v : ν
xs : List (κ × ν)
⊢ length (groupByKey ((k, v) :: xs)) = length (unique (map Prod.fst ((k, v) :: xs))) | κ : Type u_1
inst✝ : DecidableEq κ
ν : Type u_2
k : κ
v : ν
xs : List (κ × ν)
hterm : length (matchKey xs k).snd < Nat.succ (length xs)
⊢ length (groupByKey ((k, v) :: xs)) = length (unique (map Prod.fst ((k, v) :: xs))) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_groupByKey | [1294, 1] | [1316, 25] | have ih := length_groupByKey (matchKey xs k).2 | κ : Type u_1
inst✝ : DecidableEq κ
ν : Type u_2
k : κ
v : ν
xs : List (κ × ν)
hterm : length (matchKey xs k).snd < Nat.succ (length xs)
⊢ length (groupByKey ((k, v) :: xs)) = length (unique (map Prod.fst ((k, v) :: xs))) | κ : Type u_1
inst✝ : DecidableEq κ
ν : Type u_2
k : κ
v : ν
xs : List (κ × ν)
hterm : length (matchKey xs k).snd < Nat.succ (length xs)
ih : length (groupByKey (matchKey xs k).snd) = length (unique (map Prod.fst (matchKey xs k).snd))
⊢ length (groupByKey ((k, v) :: xs)) = length (unique (map Prod.fst ((k, v) :: xs))) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_groupByKey | [1294, 1] | [1316, 25] | simp only [map, unique, uniqueAux, List.not_mem_nil, ite_false, groupByKey] | κ : Type u_1
inst✝ : DecidableEq κ
ν : Type u_2
k : κ
v : ν
xs : List (κ × ν)
hterm : length (matchKey xs k).snd < Nat.succ (length xs)
ih : length (groupByKey (matchKey xs k).snd) = length (unique (map Prod.fst (matchKey xs k).snd))
⊢ length (groupByKey ((k, v) :: xs)) = length (unique (map Prod.fst ((k, v) :: xs))) | κ : Type u_1
inst✝ : DecidableEq κ
ν : Type u_2
k : κ
v : ν
xs : List (κ × ν)
hterm : length (matchKey xs k).snd < Nat.succ (length xs)
ih : length (groupByKey (matchKey xs k).snd) = length (unique (map Prod.fst (matchKey xs k).snd))
⊢ length ((k, v :: (matchKey xs k).fst) :: groupByKey (matchKey xs k).snd) = length (uniqueAux (map Prod.fst xs) [k]) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_groupByKey | [1294, 1] | [1316, 25] | simp only [length] | κ : Type u_1
inst✝ : DecidableEq κ
ν : Type u_2
k : κ
v : ν
xs : List (κ × ν)
hterm : length (matchKey xs k).snd < Nat.succ (length xs)
ih : length (groupByKey (matchKey xs k).snd) = length (unique (map Prod.fst (matchKey xs k).snd))
⊢ length ((k, v :: (matchKey xs k).fst) :: groupByKey (matchKey xs k).snd) = length (uniqueAux (map Prod.fst xs) [k]) | κ : Type u_1
inst✝ : DecidableEq κ
ν : Type u_2
k : κ
v : ν
xs : List (κ × ν)
hterm : length (matchKey xs k).snd < Nat.succ (length xs)
ih : length (groupByKey (matchKey xs k).snd) = length (unique (map Prod.fst (matchKey xs k).snd))
⊢ length (groupByKey (matchKey xs k).snd) + 1 = length (uniqueAux (map Prod.fst xs) [k]) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_groupByKey | [1294, 1] | [1316, 25] | rw [length_uniqueAux_matchKey _ k _ $ List.Mem.head _] | κ : Type u_1
inst✝ : DecidableEq κ
ν : Type u_2
k : κ
v : ν
xs : List (κ × ν)
hterm : length (matchKey xs k).snd < Nat.succ (length xs)
ih : length (groupByKey (matchKey xs k).snd) = length (unique (map Prod.fst (matchKey xs k).snd))
⊢ length (groupByKey (matchKey xs k).snd) + 1 = length (uniqueAux (map Prod.fst xs) [k]) | κ : Type u_1
inst✝ : DecidableEq κ
ν : Type u_2
k : κ
v : ν
xs : List (κ × ν)
hterm : length (matchKey xs k).snd < Nat.succ (length xs)
ih : length (groupByKey (matchKey xs k).snd) = length (unique (map Prod.fst (matchKey xs k).snd))
⊢ length (groupByKey (matchKey xs k).snd) + 1 = length (uniqueAux (map Prod.fst (matchKey xs k).snd) [k]) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_groupByKey | [1294, 1] | [1316, 25] | rw [ih] | κ : Type u_1
inst✝ : DecidableEq κ
ν : Type u_2
k : κ
v : ν
xs : List (κ × ν)
hterm : length (matchKey xs k).snd < Nat.succ (length xs)
ih : length (groupByKey (matchKey xs k).snd) = length (unique (map Prod.fst (matchKey xs k).snd))
⊢ length (groupByKey (matchKey xs k).snd) + 1 = length (uniqueAux (map Prod.fst (matchKey xs k).snd) [k]) | κ : Type u_1
inst✝ : DecidableEq κ
ν : Type u_2
k : κ
v : ν
xs : List (κ × ν)
hterm : length (matchKey xs k).snd < Nat.succ (length xs)
ih : length (groupByKey (matchKey xs k).snd) = length (unique (map Prod.fst (matchKey xs k).snd))
⊢ length (unique (map Prod.fst (matchKey xs k).snd)) + 1 = length (uniqueAux (map Prod.fst (matchKey xs k).snd) [k]) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_groupByKey | [1294, 1] | [1316, 25] | apply Eq.symm | κ : Type u_1
inst✝ : DecidableEq κ
ν : Type u_2
k : κ
v : ν
xs : List (κ × ν)
hterm : length (matchKey xs k).snd < Nat.succ (length xs)
ih : length (groupByKey (matchKey xs k).snd) = length (unique (map Prod.fst (matchKey xs k).snd))
⊢ length (unique (map Prod.fst (matchKey xs k).snd)) + 1 = length (uniqueAux (map Prod.fst (matchKey xs k).snd) [k]) | case h
κ : Type u_1
inst✝ : DecidableEq κ
ν : Type u_2
k : κ
v : ν
xs : List (κ × ν)
hterm : length (matchKey xs k).snd < Nat.succ (length xs)
ih : length (groupByKey (matchKey xs k).snd) = length (unique (map Prod.fst (matchKey xs k).snd))
⊢ length (uniqueAux (map Prod.fst (matchKey xs k).snd) [k]) = length (unique (map Prod.fst (matchKey xs k).snd)) + 1 |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_groupByKey | [1294, 1] | [1316, 25] | apply List.length_uniqueAux (acc := [k]) | case h
κ : Type u_1
inst✝ : DecidableEq κ
ν : Type u_2
k : κ
v : ν
xs : List (κ × ν)
hterm : length (matchKey xs k).snd < Nat.succ (length xs)
ih : length (groupByKey (matchKey xs k).snd) = length (unique (map Prod.fst (matchKey xs k).snd))
⊢ length (uniqueAux (map Prod.fst (matchKey xs k).snd) [k]) = length (unique (map Prod.fst (matchKey xs k).snd)) + 1 | case h.h
κ : Type u_1
inst✝ : DecidableEq κ
ν : Type u_2
k : κ
v : ν
xs : List (κ × ν)
hterm : length (matchKey xs k).snd < Nat.succ (length xs)
ih : length (groupByKey (matchKey xs k).snd) = length (unique (map Prod.fst (matchKey xs k).snd))
⊢ ∀ (x : κ), x ∈ map Prod.fst (matchKey xs k).snd → ¬x ∈ [k] |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_groupByKey | [1294, 1] | [1316, 25] | intro x | case h.h
κ : Type u_1
inst✝ : DecidableEq κ
ν : Type u_2
k : κ
v : ν
xs : List (κ × ν)
hterm : length (matchKey xs k).snd < Nat.succ (length xs)
ih : length (groupByKey (matchKey xs k).snd) = length (unique (map Prod.fst (matchKey xs k).snd))
⊢ ∀ (x : κ), x ∈ map Prod.fst (matchKey xs k).snd → ¬x ∈ [k] | case h.h
κ : Type u_1
inst✝ : DecidableEq κ
ν : Type u_2
k : κ
v : ν
xs : List (κ × ν)
hterm : length (matchKey xs k).snd < Nat.succ (length xs)
ih : length (groupByKey (matchKey xs k).snd) = length (unique (map Prod.fst (matchKey xs k).snd))
x : κ
⊢ x ∈ map Prod.fst (matchKey xs k).snd → ¬x ∈ [k] |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_groupByKey | [1294, 1] | [1316, 25] | rw [mem_singleton_iff] | case h.h
κ : Type u_1
inst✝ : DecidableEq κ
ν : Type u_2
k : κ
v : ν
xs : List (κ × ν)
hterm : length (matchKey xs k).snd < Nat.succ (length xs)
ih : length (groupByKey (matchKey xs k).snd) = length (unique (map Prod.fst (matchKey xs k).snd))
x : κ
⊢ x ∈ map Prod.fst (matchKey xs k).snd → ¬x ∈ [k] | case h.h
κ : Type u_1
inst✝ : DecidableEq κ
ν : Type u_2
k : κ
v : ν
xs : List (κ × ν)
hterm : length (matchKey xs k).snd < Nat.succ (length xs)
ih : length (groupByKey (matchKey xs k).snd) = length (unique (map Prod.fst (matchKey xs k).snd))
x : κ
⊢ x ∈ map Prod.fst (matchKey xs k).snd → ¬x = k |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_groupByKey | [1294, 1] | [1316, 25] | intro hmem hneg | case h.h
κ : Type u_1
inst✝ : DecidableEq κ
ν : Type u_2
k : κ
v : ν
xs : List (κ × ν)
hterm : length (matchKey xs k).snd < Nat.succ (length xs)
ih : length (groupByKey (matchKey xs k).snd) = length (unique (map Prod.fst (matchKey xs k).snd))
x : κ
⊢ x ∈ map Prod.fst (matchKey xs k).snd → ¬x = k | case h.h
κ : Type u_1
inst✝ : DecidableEq κ
ν : Type u_2
k : κ
v : ν
xs : List (κ × ν)
hterm : length (matchKey xs k).snd < Nat.succ (length xs)
ih : length (groupByKey (matchKey xs k).snd) = length (unique (map Prod.fst (matchKey xs k).snd))
x : κ
hmem : x ∈ map Prod.fst (matchKey xs k).snd
hneg : x = k
⊢ False |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_groupByKey | [1294, 1] | [1316, 25] | have := not_mem_matchKey_self_map_snd x xs | case h.h
κ : Type u_1
inst✝ : DecidableEq κ
ν : Type u_2
k : κ
v : ν
xs : List (κ × ν)
hterm : length (matchKey xs k).snd < Nat.succ (length xs)
ih : length (groupByKey (matchKey xs k).snd) = length (unique (map Prod.fst (matchKey xs k).snd))
x : κ
hmem : x ∈ map Prod.fst (matchKey xs k).snd
hneg : x = k
⊢ False | case h.h
κ : Type u_1
inst✝ : DecidableEq κ
ν : Type u_2
k : κ
v : ν
xs : List (κ × ν)
hterm : length (matchKey xs k).snd < Nat.succ (length xs)
ih : length (groupByKey (matchKey xs k).snd) = length (unique (map Prod.fst (matchKey xs k).snd))
x : κ
hmem : x ∈ map Prod.fst (matchKey xs k).snd
hneg : x = k
this : ¬x ∈ map Prod.fst (matchKey xs x).snd
⊢ False |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_groupByKey | [1294, 1] | [1316, 25] | rw [←hneg] at hmem | case h.h
κ : Type u_1
inst✝ : DecidableEq κ
ν : Type u_2
k : κ
v : ν
xs : List (κ × ν)
hterm : length (matchKey xs k).snd < Nat.succ (length xs)
ih : length (groupByKey (matchKey xs k).snd) = length (unique (map Prod.fst (matchKey xs k).snd))
x : κ
hmem : x ∈ map Prod.fst (matchKey xs k).snd
hneg : x = k
this : ¬x ∈ map Prod.fst (matchKey xs x).snd
⊢ False | case h.h
κ : Type u_1
inst✝ : DecidableEq κ
ν : Type u_2
k : κ
v : ν
xs : List (κ × ν)
hterm : length (matchKey xs k).snd < Nat.succ (length xs)
ih : length (groupByKey (matchKey xs k).snd) = length (unique (map Prod.fst (matchKey xs k).snd))
x : κ
hmem : x ∈ map Prod.fst (matchKey xs x).snd
hneg : x = k
this : ¬x ∈ map Prod.fst (matchKey xs x).snd
⊢ False |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_groupByKey | [1294, 1] | [1316, 25] | exact this hmem | case h.h
κ : Type u_1
inst✝ : DecidableEq κ
ν : Type u_2
k : κ
v : ν
xs : List (κ × ν)
hterm : length (matchKey xs k).snd < Nat.succ (length xs)
ih : length (groupByKey (matchKey xs k).snd) = length (unique (map Prod.fst (matchKey xs k).snd))
x : κ
hmem : x ∈ map Prod.fst (matchKey xs x).snd
hneg : x = k
this : ¬x ∈ map Prod.fst (matchKey xs x).snd
⊢ False | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_groupByKey | [1294, 1] | [1316, 25] | assumption | κ : Type u_1
inst✝ : DecidableEq κ
ν : Type u_2
xs✝ : List (κ × ν)
a✝ :
∀ (y : List (κ × ν)),
(invImage (fun a => length a) instWellFoundedRelation).1 y xs✝ →
length (groupByKey y) = length (unique (map Prod.fst y))
k : κ
v : ν
xs : List (κ × ν)
x✝ :
∀ (y : List (κ × ν)),
(invImage (fun a => length a) instWellFoundedRelation).1 y ((k, v) :: xs) →
length (groupByKey y) = length (unique (map Prod.fst y))
hterm : length (matchKey xs k).snd < Nat.succ (length xs)
⊢ (invImage (fun a => length a) instWellFoundedRelation).1 (matchKey xs k).snd ((k, v) :: xs) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.matchKey_snd_sublist | [1324, 1] | [1331, 74] | simp only [matchKey, h, ite_true] | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
kv : κ × ν
kvs : List (κ × ν)
ih : (matchKey kvs k).snd <+ kvs
h : kv.fst = k
⊢ (matchKey (kv :: kvs) k).snd <+ kv :: kvs | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
kv : κ × ν
kvs : List (κ × ν)
ih : (matchKey kvs k).snd <+ kvs
h : kv.fst = k
⊢ (matchKey kvs k).snd <+ kv :: kvs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.matchKey_snd_sublist | [1324, 1] | [1331, 74] | exact Sublist.cons _ _ _ ih | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
kv : κ × ν
kvs : List (κ × ν)
ih : (matchKey kvs k).snd <+ kvs
h : kv.fst = k
⊢ (matchKey kvs k).snd <+ kv :: kvs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.matchKey_snd_sublist | [1324, 1] | [1331, 74] | simp only [matchKey, h, ite_true] | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
kv : κ × ν
kvs : List (κ × ν)
ih : (matchKey kvs k).snd <+ kvs
h : ¬kv.fst = k
⊢ (matchKey (kv :: kvs) k).snd <+ kv :: kvs | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
kv : κ × ν
kvs : List (κ × ν)
ih : (matchKey kvs k).snd <+ kvs
h : ¬kv.fst = k
⊢ (if False then (kv.snd :: (matchKey kvs k).fst, (matchKey kvs k).snd)
else ((matchKey kvs k).fst, (kv.fst, kv.snd) :: (matchKey kvs k).snd)).snd <+
kv :: kvs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.matchKey_snd_sublist | [1324, 1] | [1331, 74] | exact Sublist.cons2 _ _ _ ih | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
kv : κ × ν
kvs : List (κ × ν)
ih : (matchKey kvs k).snd <+ kvs
h : ¬kv.fst = k
⊢ (if False then (kv.snd :: (matchKey kvs k).fst, (matchKey kvs k).snd)
else ((matchKey kvs k).fst, (kv.fst, kv.snd) :: (matchKey kvs k).snd)).snd <+
kv :: kvs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.matchKey_snd_sublist_of_sublist | [1333, 1] | [1350, 35] | intro k xs ys h | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
⊢ ∀ (k : κ) (xs ys : List (κ × ν)), xs <+ ys → (matchKey xs k).snd <+ (matchKey ys k).snd | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
xs ys : List (κ × ν)
h : xs <+ ys
⊢ (matchKey xs k).snd <+ (matchKey ys k).snd |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.matchKey_snd_sublist_of_sublist | [1333, 1] | [1350, 35] | induction h with
| nil => constructor
| cons xs' ys' x' h' ih =>
simp only [matchKey]
cases Decidable.em (x'.fst = k) with
| inl heq => simp only [heq, ite_true]; apply ih
| inr hneq => simp only [hneq, ite_false]; apply Sublist.cons _ _ _ ih
| cons2 xs' ys' x' h' ih =>
simp only [matchKey]
cases Decidable.em (x'.fst = k) with
| inl heq => simp only [heq, ite_true]; assumption
| inr hneq =>
simp only [hneq, ite_false]
apply Sublist.cons2 _ _ _ ih | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
xs ys : List (κ × ν)
h : xs <+ ys
⊢ (matchKey xs k).snd <+ (matchKey ys k).snd | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.matchKey_snd_sublist_of_sublist | [1333, 1] | [1350, 35] | constructor | case nil
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
xs ys : List (κ × ν)
⊢ (matchKey [] k).snd <+ (matchKey [] k).snd | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.matchKey_snd_sublist_of_sublist | [1333, 1] | [1350, 35] | simp only [matchKey] | case cons
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
xs ys : List (κ × ν)
xs' ys' : List (κ × ν)
x' : κ × ν
h' : xs' <+ ys'
ih : (matchKey xs' k).snd <+ (matchKey ys' k).snd
⊢ (matchKey xs' k).snd <+ (matchKey (x' :: ys') k).snd | case cons
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
xs ys : List (κ × ν)
xs' ys' : List (κ × ν)
x' : κ × ν
h' : xs' <+ ys'
ih : (matchKey xs' k).snd <+ (matchKey ys' k).snd
⊢ (matchKey xs' k).snd <+
(if x'.fst = k then (x'.snd :: (matchKey ys' k).fst, (matchKey ys' k).snd)
else ((matchKey ys' k).fst, (x'.fst, x'.snd) :: (matchKey ys' k).snd)).snd |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.matchKey_snd_sublist_of_sublist | [1333, 1] | [1350, 35] | cases Decidable.em (x'.fst = k) with
| inl heq => simp only [heq, ite_true]; apply ih
| inr hneq => simp only [hneq, ite_false]; apply Sublist.cons _ _ _ ih | case cons
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
xs ys : List (κ × ν)
xs' ys' : List (κ × ν)
x' : κ × ν
h' : xs' <+ ys'
ih : (matchKey xs' k).snd <+ (matchKey ys' k).snd
⊢ (matchKey xs' k).snd <+
(if x'.fst = k then (x'.snd :: (matchKey ys' k).fst, (matchKey ys' k).snd)
else ((matchKey ys' k).fst, (x'.fst, x'.snd) :: (matchKey ys' k).snd)).snd | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.matchKey_snd_sublist_of_sublist | [1333, 1] | [1350, 35] | simp only [heq, ite_true] | case cons.inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
xs ys : List (κ × ν)
xs' ys' : List (κ × ν)
x' : κ × ν
h' : xs' <+ ys'
ih : (matchKey xs' k).snd <+ (matchKey ys' k).snd
heq : x'.fst = k
⊢ (matchKey xs' k).snd <+
(if x'.fst = k then (x'.snd :: (matchKey ys' k).fst, (matchKey ys' k).snd)
else ((matchKey ys' k).fst, (x'.fst, x'.snd) :: (matchKey ys' k).snd)).snd | case cons.inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
xs ys : List (κ × ν)
xs' ys' : List (κ × ν)
x' : κ × ν
h' : xs' <+ ys'
ih : (matchKey xs' k).snd <+ (matchKey ys' k).snd
heq : x'.fst = k
⊢ (matchKey xs' k).snd <+ (matchKey ys' k).snd |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.matchKey_snd_sublist_of_sublist | [1333, 1] | [1350, 35] | apply ih | case cons.inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
xs ys : List (κ × ν)
xs' ys' : List (κ × ν)
x' : κ × ν
h' : xs' <+ ys'
ih : (matchKey xs' k).snd <+ (matchKey ys' k).snd
heq : x'.fst = k
⊢ (matchKey xs' k).snd <+ (matchKey ys' k).snd | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.matchKey_snd_sublist_of_sublist | [1333, 1] | [1350, 35] | simp only [hneq, ite_false] | case cons.inr
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
xs ys : List (κ × ν)
xs' ys' : List (κ × ν)
x' : κ × ν
h' : xs' <+ ys'
ih : (matchKey xs' k).snd <+ (matchKey ys' k).snd
hneq : ¬x'.fst = k
⊢ (matchKey xs' k).snd <+
(if x'.fst = k then (x'.snd :: (matchKey ys' k).fst, (matchKey ys' k).snd)
else ((matchKey ys' k).fst, (x'.fst, x'.snd) :: (matchKey ys' k).snd)).snd | case cons.inr
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
xs ys : List (κ × ν)
xs' ys' : List (κ × ν)
x' : κ × ν
h' : xs' <+ ys'
ih : (matchKey xs' k).snd <+ (matchKey ys' k).snd
hneq : ¬x'.fst = k
⊢ (matchKey xs' k).snd <+ (x'.fst, x'.snd) :: (matchKey ys' k).snd |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.matchKey_snd_sublist_of_sublist | [1333, 1] | [1350, 35] | apply Sublist.cons _ _ _ ih | case cons.inr
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
xs ys : List (κ × ν)
xs' ys' : List (κ × ν)
x' : κ × ν
h' : xs' <+ ys'
ih : (matchKey xs' k).snd <+ (matchKey ys' k).snd
hneq : ¬x'.fst = k
⊢ (matchKey xs' k).snd <+ (x'.fst, x'.snd) :: (matchKey ys' k).snd | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.matchKey_snd_sublist_of_sublist | [1333, 1] | [1350, 35] | simp only [matchKey] | case cons2
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
xs ys : List (κ × ν)
xs' ys' : List (κ × ν)
x' : κ × ν
h' : xs' <+ ys'
ih : (matchKey xs' k).snd <+ (matchKey ys' k).snd
⊢ (matchKey (x' :: xs') k).snd <+ (matchKey (x' :: ys') k).snd | case cons2
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
xs ys : List (κ × ν)
xs' ys' : List (κ × ν)
x' : κ × ν
h' : xs' <+ ys'
ih : (matchKey xs' k).snd <+ (matchKey ys' k).snd
⊢ (if x'.fst = k then (x'.snd :: (matchKey xs' k).fst, (matchKey xs' k).snd)
else ((matchKey xs' k).fst, (x'.fst, x'.snd) :: (matchKey xs' k).snd)).snd <+
(if x'.fst = k then (x'.snd :: (matchKey ys' k).fst, (matchKey ys' k).snd)
else ((matchKey ys' k).fst, (x'.fst, x'.snd) :: (matchKey ys' k).snd)).snd |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.matchKey_snd_sublist_of_sublist | [1333, 1] | [1350, 35] | cases Decidable.em (x'.fst = k) with
| inl heq => simp only [heq, ite_true]; assumption
| inr hneq =>
simp only [hneq, ite_false]
apply Sublist.cons2 _ _ _ ih | case cons2
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
xs ys : List (κ × ν)
xs' ys' : List (κ × ν)
x' : κ × ν
h' : xs' <+ ys'
ih : (matchKey xs' k).snd <+ (matchKey ys' k).snd
⊢ (if x'.fst = k then (x'.snd :: (matchKey xs' k).fst, (matchKey xs' k).snd)
else ((matchKey xs' k).fst, (x'.fst, x'.snd) :: (matchKey xs' k).snd)).snd <+
(if x'.fst = k then (x'.snd :: (matchKey ys' k).fst, (matchKey ys' k).snd)
else ((matchKey ys' k).fst, (x'.fst, x'.snd) :: (matchKey ys' k).snd)).snd | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.matchKey_snd_sublist_of_sublist | [1333, 1] | [1350, 35] | simp only [heq, ite_true] | case cons2.inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
xs ys : List (κ × ν)
xs' ys' : List (κ × ν)
x' : κ × ν
h' : xs' <+ ys'
ih : (matchKey xs' k).snd <+ (matchKey ys' k).snd
heq : x'.fst = k
⊢ (if x'.fst = k then (x'.snd :: (matchKey xs' k).fst, (matchKey xs' k).snd)
else ((matchKey xs' k).fst, (x'.fst, x'.snd) :: (matchKey xs' k).snd)).snd <+
(if x'.fst = k then (x'.snd :: (matchKey ys' k).fst, (matchKey ys' k).snd)
else ((matchKey ys' k).fst, (x'.fst, x'.snd) :: (matchKey ys' k).snd)).snd | case cons2.inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
xs ys : List (κ × ν)
xs' ys' : List (κ × ν)
x' : κ × ν
h' : xs' <+ ys'
ih : (matchKey xs' k).snd <+ (matchKey ys' k).snd
heq : x'.fst = k
⊢ (matchKey xs' k).snd <+ (matchKey ys' k).snd |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.matchKey_snd_sublist_of_sublist | [1333, 1] | [1350, 35] | assumption | case cons2.inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
xs ys : List (κ × ν)
xs' ys' : List (κ × ν)
x' : κ × ν
h' : xs' <+ ys'
ih : (matchKey xs' k).snd <+ (matchKey ys' k).snd
heq : x'.fst = k
⊢ (matchKey xs' k).snd <+ (matchKey ys' k).snd | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.matchKey_snd_sublist_of_sublist | [1333, 1] | [1350, 35] | simp only [hneq, ite_false] | case cons2.inr
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
xs ys : List (κ × ν)
xs' ys' : List (κ × ν)
x' : κ × ν
h' : xs' <+ ys'
ih : (matchKey xs' k).snd <+ (matchKey ys' k).snd
hneq : ¬x'.fst = k
⊢ (if x'.fst = k then (x'.snd :: (matchKey xs' k).fst, (matchKey xs' k).snd)
else ((matchKey xs' k).fst, (x'.fst, x'.snd) :: (matchKey xs' k).snd)).snd <+
(if x'.fst = k then (x'.snd :: (matchKey ys' k).fst, (matchKey ys' k).snd)
else ((matchKey ys' k).fst, (x'.fst, x'.snd) :: (matchKey ys' k).snd)).snd | case cons2.inr
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
xs ys : List (κ × ν)
xs' ys' : List (κ × ν)
x' : κ × ν
h' : xs' <+ ys'
ih : (matchKey xs' k).snd <+ (matchKey ys' k).snd
hneq : ¬x'.fst = k
⊢ (x'.fst, x'.snd) :: (matchKey xs' k).snd <+ (x'.fst, x'.snd) :: (matchKey ys' k).snd |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.matchKey_snd_sublist_of_sublist | [1333, 1] | [1350, 35] | apply Sublist.cons2 _ _ _ ih | case cons2.inr
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
xs ys : List (κ × ν)
xs' ys' : List (κ × ν)
x' : κ × ν
h' : xs' <+ ys'
ih : (matchKey xs' k).snd <+ (matchKey ys' k).snd
hneq : ¬x'.fst = k
⊢ (x'.fst, x'.snd) :: (matchKey xs' k).snd <+ (x'.fst, x'.snd) :: (matchKey ys' k).snd | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.fst_groupByKey_sublist | [1359, 1] | [1369, 25] | assumption | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
kvs : List (κ × ν)
a✝ :
∀ (y : List (κ × ν)),
(invImage (fun a => length a) instWellFoundedRelation).1 y kvs → map Prod.fst (groupByKey y) <+ map Prod.fst y
k : κ
v : ν
xs : List (κ × ν)
x✝ :
∀ (y : List (κ × ν)),
(invImage (fun a => length a) instWellFoundedRelation).1 y ((k, v) :: xs) →
map Prod.fst (groupByKey y) <+ map Prod.fst y
hterm : length (matchKey xs k).snd < Nat.succ (length xs)
⊢ (invImage (fun a => length a) instWellFoundedRelation).1 (matchKey xs k).snd ((k, v) :: xs) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_matchKey_key_or_snd | [1373, 1] | [1418, 25] | simp only [matchKey] | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
⊢ x ∈ map Prod.fst (matchKey ((k', v) :: ys) k).snd | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
⊢ x ∈
map Prod.fst
(if k' = k then (v :: (matchKey ys k).fst, (matchKey ys k).snd)
else ((matchKey ys k).fst, (k', v) :: (matchKey ys k).snd)).snd |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_matchKey_key_or_snd | [1373, 1] | [1418, 25] | cases Decidable.em (k' = k) with
| inl hkeq =>
simp only [hkeq, ite_true]
have : x ∈ map Prod.fst ys := by
cases hx with
| head => contradiction
| tail => assumption
have ih := mem_fst_matchKey_key_or_snd this k
cases ih with
| inl => contradiction
| inr hmem => exact hmem
| inr hkneq =>
simp only [hkneq, ite_false]
simp only [map]
cases Decidable.em (x = k') with
| inl hxeq => rw [hxeq]; apply Mem.head
| inr hxneq =>
apply Mem.tail
have : x ∈ map Prod.fst (matchKey ys k).snd := by
cases hx with
| head => contradiction
| tail _ htail =>
have := mem_fst_matchKey_key_or_snd htail k
cases this with
| inl => contradiction
| inr => assumption
have ih := mem_fst_matchKey_key_or_snd this k'
cases ih with
| inl => contradiction
| inr => assumption | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
⊢ x ∈
map Prod.fst
(if k' = k then (v :: (matchKey ys k).fst, (matchKey ys k).snd)
else ((matchKey ys k).fst, (k', v) :: (matchKey ys k).snd)).snd | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_matchKey_key_or_snd | [1373, 1] | [1418, 25] | simp only [hkeq, ite_true] | case inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkeq : k' = k
⊢ x ∈
map Prod.fst
(if k' = k then (v :: (matchKey ys k).fst, (matchKey ys k).snd)
else ((matchKey ys k).fst, (k', v) :: (matchKey ys k).snd)).snd | case inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkeq : k' = k
⊢ x ∈ map Prod.fst (matchKey ys k).snd |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_matchKey_key_or_snd | [1373, 1] | [1418, 25] | have : x ∈ map Prod.fst ys := by
cases hx with
| head => contradiction
| tail => assumption | case inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkeq : k' = k
⊢ x ∈ map Prod.fst (matchKey ys k).snd | case inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkeq : k' = k
this : x ∈ map Prod.fst ys
⊢ x ∈ map Prod.fst (matchKey ys k).snd |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_matchKey_key_or_snd | [1373, 1] | [1418, 25] | have ih := mem_fst_matchKey_key_or_snd this k | case inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkeq : k' = k
this : x ∈ map Prod.fst ys
⊢ x ∈ map Prod.fst (matchKey ys k).snd | case inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkeq : k' = k
this : x ∈ map Prod.fst ys
ih : x = k ∨ x ∈ map Prod.fst (matchKey ys k).snd
⊢ x ∈ map Prod.fst (matchKey ys k).snd |
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