Datasets:
internlm
/
Lean-Github

Dataset card Data Studio Files Community
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https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/Proofs.lean
groupBySubtractive_spec4
[1140, 1]
[1172, 45]
. cases y . rfl . contradiction
case hf.none η : Type u_η dec_η : DecidableEq η sch : Schema τ : Type u_1 inst : DecidableEq τ t : Table sch c : η hc : Schema.HasCol (c, τ) sch y : Option τ hxy : Option.map ULift.up none = Option.map ULift.up y ⊢ none = y case hf.some η : Type u_η dec_η : DecidableEq η sch : Schema τ : Type u_1 inst : DecidableEq τ t : Table sch c : η hc : Schema.HasCol (c, τ) sch y : Option τ val✝ : τ hxy : Option.map ULift.up (some val✝) = Option.map ULift.up y ⊢ some val✝ = y
case hf.some η : Type u_η dec_η : DecidableEq η sch : Schema τ : Type u_1 inst : DecidableEq τ t : Table sch c : η hc : Schema.HasCol (c, τ) sch y : Option τ val✝ : τ hxy : Option.map ULift.up (some val✝) = Option.map ULift.up y ⊢ some val✝ = y
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/Proofs.lean
groupBySubtractive_spec4
[1140, 1]
[1172, 45]
. cases y . contradiction . cases hxy; rfl
case hf.some η : Type u_η dec_η : DecidableEq η sch : Schema τ : Type u_1 inst : DecidableEq τ t : Table sch c : η hc : Schema.HasCol (c, τ) sch y : Option τ val✝ : τ hxy : Option.map ULift.up (some val✝) = Option.map ULift.up y ⊢ some val✝ = y
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/Proofs.lean
groupBySubtractive_spec4
[1140, 1]
[1172, 45]
cases y
case hf.none η : Type u_η dec_η : DecidableEq η sch : Schema τ : Type u_1 inst : DecidableEq τ t : Table sch c : η hc : Schema.HasCol (c, τ) sch y : Option τ hxy : Option.map ULift.up none = Option.map ULift.up y ⊢ none = y
case hf.none.none η : Type u_η dec_η : DecidableEq η sch : Schema τ : Type u_1 inst : DecidableEq τ t : Table sch c : η hc : Schema.HasCol (c, τ) sch hxy : Option.map ULift.up none = Option.map ULift.up none ⊢ none = none case hf.none.some η : Type u_η dec_η : DecidableEq η sch : Schema τ : Type u_1 inst : DecidableEq τ t : Table sch c : η hc : Schema.HasCol (c, τ) sch val✝ : τ hxy : Option.map ULift.up none = Option.map ULift.up (some val✝) ⊢ none = some val✝
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/Proofs.lean
groupBySubtractive_spec4
[1140, 1]
[1172, 45]
. rfl
case hf.none.none η : Type u_η dec_η : DecidableEq η sch : Schema τ : Type u_1 inst : DecidableEq τ t : Table sch c : η hc : Schema.HasCol (c, τ) sch hxy : Option.map ULift.up none = Option.map ULift.up none ⊢ none = none case hf.none.some η : Type u_η dec_η : DecidableEq η sch : Schema τ : Type u_1 inst : DecidableEq τ t : Table sch c : η hc : Schema.HasCol (c, τ) sch val✝ : τ hxy : Option.map ULift.up none = Option.map ULift.up (some val✝) ⊢ none = some val✝
case hf.none.some η : Type u_η dec_η : DecidableEq η sch : Schema τ : Type u_1 inst : DecidableEq τ t : Table sch c : η hc : Schema.HasCol (c, τ) sch val✝ : τ hxy : Option.map ULift.up none = Option.map ULift.up (some val✝) ⊢ none = some val✝
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/Proofs.lean
groupBySubtractive_spec4
[1140, 1]
[1172, 45]
. contradiction
case hf.none.some η : Type u_η dec_η : DecidableEq η sch : Schema τ : Type u_1 inst : DecidableEq τ t : Table sch c : η hc : Schema.HasCol (c, τ) sch val✝ : τ hxy : Option.map ULift.up none = Option.map ULift.up (some val✝) ⊢ none = some val✝
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/Proofs.lean
groupBySubtractive_spec4
[1140, 1]
[1172, 45]
rfl
case hf.none.none η : Type u_η dec_η : DecidableEq η sch : Schema τ : Type u_1 inst : DecidableEq τ t : Table sch c : η hc : Schema.HasCol (c, τ) sch hxy : Option.map ULift.up none = Option.map ULift.up none ⊢ none = none
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/Proofs.lean
groupBySubtractive_spec4
[1140, 1]
[1172, 45]
contradiction
case hf.none.some η : Type u_η dec_η : DecidableEq η sch : Schema τ : Type u_1 inst : DecidableEq τ t : Table sch c : η hc : Schema.HasCol (c, τ) sch val✝ : τ hxy : Option.map ULift.up none = Option.map ULift.up (some val✝) ⊢ none = some val✝
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/Proofs.lean
groupBySubtractive_spec4
[1140, 1]
[1172, 45]
cases y
case hf.some η : Type u_η dec_η : DecidableEq η sch : Schema τ : Type u_1 inst : DecidableEq τ t : Table sch c : η hc : Schema.HasCol (c, τ) sch y : Option τ val✝ : τ hxy : Option.map ULift.up (some val✝) = Option.map ULift.up y ⊢ some val✝ = y
case hf.some.none η : Type u_η dec_η : DecidableEq η sch : Schema τ : Type u_1 inst : DecidableEq τ t : Table sch c : η hc : Schema.HasCol (c, τ) sch val✝ : τ hxy : Option.map ULift.up (some val✝) = Option.map ULift.up none ⊢ some val✝ = none case hf.some.some η : Type u_η dec_η : DecidableEq η sch : Schema τ : Type u_1 inst : DecidableEq τ t : Table sch c : η hc : Schema.HasCol (c, τ) sch val✝¹ val✝ : τ hxy : Option.map ULift.up (some val✝¹) = Option.map ULift.up (some val✝) ⊢ some val✝¹ = some val✝
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/Proofs.lean
groupBySubtractive_spec4
[1140, 1]
[1172, 45]
. contradiction
case hf.some.none η : Type u_η dec_η : DecidableEq η sch : Schema τ : Type u_1 inst : DecidableEq τ t : Table sch c : η hc : Schema.HasCol (c, τ) sch val✝ : τ hxy : Option.map ULift.up (some val✝) = Option.map ULift.up none ⊢ some val✝ = none case hf.some.some η : Type u_η dec_η : DecidableEq η sch : Schema τ : Type u_1 inst : DecidableEq τ t : Table sch c : η hc : Schema.HasCol (c, τ) sch val✝¹ val✝ : τ hxy : Option.map ULift.up (some val✝¹) = Option.map ULift.up (some val✝) ⊢ some val✝¹ = some val✝
case hf.some.some η : Type u_η dec_η : DecidableEq η sch : Schema τ : Type u_1 inst : DecidableEq τ t : Table sch c : η hc : Schema.HasCol (c, τ) sch val✝¹ val✝ : τ hxy : Option.map ULift.up (some val✝¹) = Option.map ULift.up (some val✝) ⊢ some val✝¹ = some val✝
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/Proofs.lean
groupBySubtractive_spec4
[1140, 1]
[1172, 45]
. cases hxy; rfl
case hf.some.some η : Type u_η dec_η : DecidableEq η sch : Schema τ : Type u_1 inst : DecidableEq τ t : Table sch c : η hc : Schema.HasCol (c, τ) sch val✝¹ val✝ : τ hxy : Option.map ULift.up (some val✝¹) = Option.map ULift.up (some val✝) ⊢ some val✝¹ = some val✝
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/Proofs.lean
groupBySubtractive_spec4
[1140, 1]
[1172, 45]
contradiction
case hf.some.none η : Type u_η dec_η : DecidableEq η sch : Schema τ : Type u_1 inst : DecidableEq τ t : Table sch c : η hc : Schema.HasCol (c, τ) sch val✝ : τ hxy : Option.map ULift.up (some val✝) = Option.map ULift.up none ⊢ some val✝ = none
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/Proofs.lean
groupBySubtractive_spec4
[1140, 1]
[1172, 45]
cases hxy
case hf.some.some η : Type u_η dec_η : DecidableEq η sch : Schema τ : Type u_1 inst : DecidableEq τ t : Table sch c : η hc : Schema.HasCol (c, τ) sch val✝¹ val✝ : τ hxy : Option.map ULift.up (some val✝¹) = Option.map ULift.up (some val✝) ⊢ some val✝¹ = some val✝
case hf.some.some.refl η : Type u_η dec_η : DecidableEq η sch : Schema τ : Type u_1 inst : DecidableEq τ t : Table sch c : η hc : Schema.HasCol (c, τ) sch val✝ : τ ⊢ some val✝ = some val✝
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/Proofs.lean
groupBySubtractive_spec4
[1140, 1]
[1172, 45]
rfl
case hf.some.some.refl η : Type u_η dec_η : DecidableEq η sch : Schema τ : Type u_1 inst : DecidableEq τ t : Table sch c : η hc : Schema.HasCol (c, τ) sch val✝ : τ ⊢ some val✝ = some val✝
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/Proofs.lean
groupBySubtractive_spec4
[1140, 1]
[1172, 45]
apply List.groupByKey_fsts_no_duplicates
case hxs η : Type u_η dec_η : DecidableEq η sch : Schema τ : Type u_1 inst : DecidableEq τ t : Table sch c : η hc : Schema.HasCol (c, τ) sch ⊢ List.NoDuplicates (List.map Prod.fst (List.groupByKey (List.map (fun r => (Cell.toOption (Row.getCell r hc), r)) t.rows)))
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/Proofs.lean
update_spec4
[1221, 1]
[1227, 24]
intros
η : Type u_η dec_η : DecidableEq η sch : Schema ⊢ ∀ (subsch : RetypedSubschema sch) (t : Table sch) (f : Row sch → Row (RetypedSubschema.toSchema subsch)), nrows (update subsch t f) = nrows t
η : Type u_η dec_η : DecidableEq η sch : Schema subsch✝ : RetypedSubschema sch t✝ : Table sch f✝ : Row sch → Row (RetypedSubschema.toSchema subsch✝) ⊢ nrows (update subsch✝ t✝ f✝) = nrows t✝
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/Proofs.lean
update_spec4
[1221, 1]
[1227, 24]
simp only [nrows, update, Schema.length_eq_List_length]
η : Type u_η dec_η : DecidableEq η sch : Schema subsch✝ : RetypedSubschema sch t✝ : Table sch f✝ : Row sch → Row (RetypedSubschema.toSchema subsch✝) ⊢ nrows (update subsch✝ t✝ f✝) = nrows t✝
η : Type u_η dec_η : DecidableEq η sch : Schema subsch✝ : RetypedSubschema sch t✝ : Table sch f✝ : Row sch → Row (RetypedSubschema.toSchema subsch✝) ⊢ List.length (List.map (fun r => update.updateCells r (f✝ r)) t✝.rows) = List.length t✝.rows
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/Proofs.lean
update_spec4
[1221, 1]
[1227, 24]
apply List.length_map
η : Type u_η dec_η : DecidableEq η sch : Schema subsch✝ : RetypedSubschema sch t✝ : Table sch f✝ : Row sch → Row (RetypedSubschema.toSchema subsch✝) ⊢ List.length (List.map (fun r => update.updateCells r (f✝ r)) t✝.rows) = List.length t✝.rows
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/Proofs.lean
select_spec4
[1232, 1]
[1237, 68]
intros
η : Type u_η dec_η : DecidableEq η sch : Schema sch' : Schema ⊢ ∀ (t : Table sch) (f : Row sch → Fin (nrows t) → Row sch'), nrows (select t f) = nrows t
η : Type u_η dec_η : DecidableEq η sch : Schema sch' : Schema t✝ : Table sch f✝ : Row sch → Fin (nrows t✝) → Row sch' ⊢ nrows (select t✝ f✝) = nrows t✝
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/Proofs.lean
select_spec4
[1232, 1]
[1237, 68]
simp only [nrows, select, Schema.length_eq_List_length]
η : Type u_η dec_η : DecidableEq η sch : Schema sch' : Schema t✝ : Table sch f✝ : Row sch → Fin (nrows t✝) → Row sch' ⊢ nrows (select t✝ f✝) = nrows t✝
η : Type u_η dec_η : DecidableEq η sch : Schema sch' : Schema t✝ : Table sch f✝ : Row sch → Fin (nrows t✝) → Row sch' ⊢ List.length (List.map (fun x => f✝ x.snd ((_ : List.length t✝.rows = nrows t✝) ▸ x.fst)) (List.verifiedEnum t✝.rows)) = List.length t✝.rows
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/Proofs.lean
select_spec4
[1232, 1]
[1237, 68]
exact Eq.trans (List.length_map _ _) (List.length_verifiedEnum _)
η : Type u_η dec_η : DecidableEq η sch : Schema sch' : Schema t✝ : Table sch f✝ : Row sch → Fin (nrows t✝) → Row sch' ⊢ List.length (List.map (fun x => f✝ x.snd ((_ : List.length t✝.rows = nrows t✝) ▸ x.fst)) (List.verifiedEnum t✝.rows)) = List.length t✝.rows
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.map_eq_List_map
[33, 1]
[39, 24]
funext _ _ _ xs
η : Type u_η dec_η : DecidableEq η schema : Schema ⊢ @map = @List.map
case h.h.h.h η : Type u_η dec_η : DecidableEq η schema : Schema x✝² : Type u_2 x✝¹ : Type u_1 x✝ : x✝² → x✝¹ xs : List x✝² ⊢ map x✝ xs = List.map x✝ xs
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.map_eq_List_map
[33, 1]
[39, 24]
induction xs with | nil => rfl | cons _ _ ih => simp only [map, List.map] exact congrArg _ ih
case h.h.h.h η : Type u_η dec_η : DecidableEq η schema : Schema x✝² : Type u_2 x✝¹ : Type u_1 x✝ : x✝² → x✝¹ xs : List x✝² ⊢ map x✝ xs = List.map x✝ xs
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.map_eq_List_map
[33, 1]
[39, 24]
rfl
case h.h.h.h.nil η : Type u_η dec_η : DecidableEq η schema : Schema x✝² : Type u_2 x✝¹ : Type u_1 x✝ : x✝² → x✝¹ ⊢ map x✝ [] = List.map x✝ []
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.map_eq_List_map
[33, 1]
[39, 24]
simp only [map, List.map]
case h.h.h.h.cons η : Type u_η dec_η : DecidableEq η schema : Schema x✝² : Type u_2 x✝¹ : Type u_1 x✝ : x✝² → x✝¹ head✝ : x✝² tail✝ : List x✝² ih : map x✝ tail✝ = List.map x✝ tail✝ ⊢ map x✝ (head✝ :: tail✝) = List.map x✝ (head✝ :: tail✝)
case h.h.h.h.cons η : Type u_η dec_η : DecidableEq η schema : Schema x✝² : Type u_2 x✝¹ : Type u_1 x✝ : x✝² → x✝¹ head✝ : x✝² tail✝ : List x✝² ih : map x✝ tail✝ = List.map x✝ tail✝ ⊢ x✝ head✝ :: map x✝ tail✝ = x✝ head✝ :: List.map x✝ tail✝
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.map_eq_List_map
[33, 1]
[39, 24]
exact congrArg _ ih
case h.h.h.h.cons η : Type u_η dec_η : DecidableEq η schema : Schema x✝² : Type u_2 x✝¹ : Type u_1 x✝ : x✝² → x✝¹ head✝ : x✝² tail✝ : List x✝² ih : map x✝ tail✝ = List.map x✝ tail✝ ⊢ x✝ head✝ :: map x✝ tail✝ = x✝ head✝ :: List.map x✝ tail✝
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.length_eq_List_length
[46, 1]
[52, 24]
funext _ xs
η : Type u_η dec_η : DecidableEq η schema : Schema ⊢ @length = @List.length
case h.h η : Type u_η dec_η : DecidableEq η schema : Schema x✝ : Type u_1 xs : List x✝ ⊢ length xs = List.length xs
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.length_eq_List_length
[46, 1]
[52, 24]
induction xs with | nil => rfl | cons _ _ ih => simp only [length, List.length] exact congrArg _ ih
case h.h η : Type u_η dec_η : DecidableEq η schema : Schema x✝ : Type u_1 xs : List x✝ ⊢ length xs = List.length xs
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.length_eq_List_length
[46, 1]
[52, 24]
rfl
case h.h.nil η : Type u_η dec_η : DecidableEq η schema : Schema x✝ : Type u_1 ⊢ length [] = List.length []
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.length_eq_List_length
[46, 1]
[52, 24]
simp only [length, List.length]
case h.h.cons η : Type u_η dec_η : DecidableEq η schema : Schema x✝ : Type u_1 head✝ : x✝ tail✝ : List x✝ ih : length tail✝ = List.length tail✝ ⊢ length (head✝ :: tail✝) = List.length (head✝ :: tail✝)
case h.h.cons η : Type u_η dec_η : DecidableEq η schema : Schema x✝ : Type u_1 head✝ : x✝ tail✝ : List x✝ ih : length tail✝ = List.length tail✝ ⊢ length tail✝ + 1 = List.length tail✝ + 1
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.length_eq_List_length
[46, 1]
[52, 24]
exact congrArg _ ih
case h.h.cons η : Type u_η dec_η : DecidableEq η schema : Schema x✝ : Type u_1 head✝ : x✝ tail✝ : List x✝ ih : length tail✝ = List.length tail✝ ⊢ length tail✝ + 1 = List.length tail✝ + 1
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.length_nths
[71, 1]
[74, 24]
rw [nths, Schema.map_eq_List_map]
η : Type u_η dec_η : DecidableEq η schema : Schema α : Type u_1 xs : List α ns : List (Fin (length xs)) ⊢ List.length (nths xs ns) = List.length ns
η : Type u_η dec_η : DecidableEq η schema : Schema α : Type u_1 xs : List α ns : List (Fin (length xs)) ⊢ List.length (List.map (fun n => nth xs n.val (_ : n.val < length xs)) ns) = List.length ns
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.length_nths
[71, 1]
[74, 24]
apply List.length_map
η : Type u_η dec_η : DecidableEq η schema : Schema α : Type u_1 xs : List α ns : List (Fin (length xs)) ⊢ List.length (List.map (fun n => nth xs n.val (_ : n.val < length xs)) ns) = List.length ns
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.sieve_eq_List_sieve
[83, 1]
[90, 11]
simp only [sieve, List.sieve]
η : Type u_η dec_η : DecidableEq η schema : Schema τ : Type u_1 bs : List Bool xs✝ xs : List τ ⊢ sieve [] xs = List.sieve [] xs
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.sieve_eq_List_sieve
[83, 1]
[90, 11]
simp only [sieve, List.sieve]
η : Type u_η dec_η : DecidableEq η schema : Schema τ : Type u_1 bs : List Bool xs : List τ head✝ : Bool tail✝ : List Bool ⊢ sieve (head✝ :: tail✝) [] = List.sieve (head✝ :: tail✝) []
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.get_map_nths_eq_get_get
[106, 1]
[126, 11]
simp only [nths, map, get]
η : Type u_η dec_η : DecidableEq η schema : Schema α : Type u_1 β : Type u_2 xs : List (α × β) n : Fin (length xs) ns : List (Fin (length xs)) hi : 0 < List.length (n :: ns) ⊢ List.get (List.map Prod.fst (nths xs (n :: ns))) { val := 0, isLt := (_ : 0 < List.length (List.map Prod.fst (nths xs (n :: ns)))) } = List.get (List.map Prod.fst xs) { val := (List.get (n :: ns) { val := 0, isLt := hi }).val, isLt := (_ : (List.get (n :: ns) { val := 0, isLt := hi }).val < List.length (List.map Prod.fst xs)) }
η : Type u_η dec_η : DecidableEq η schema : Schema α : Type u_1 β : Type u_2 xs : List (α × β) n : Fin (length xs) ns : List (Fin (length xs)) hi : 0 < List.length (n :: ns) ⊢ List.get (List.map Prod.fst (nth xs n.val (_ : n.val < length xs) :: map (fun n => nth xs n.val (_ : n.val < length xs)) ns)) { val := 0, isLt := (_ : 0 < List.length (List.map Prod.fst (nths xs (n :: ns)))) } = List.get (List.map Prod.fst xs) { val := (List.get (n :: ns) { val := 0, isLt := hi }).val, isLt := (_ : (List.get (n :: ns) { val := 0, isLt := hi }).val < List.length (List.map Prod.fst xs)) }
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.get_map_nths_eq_get_get
[106, 1]
[126, 11]
rw [nth_eq_get]
η : Type u_η dec_η : DecidableEq η schema : Schema α : Type u_1 β : Type u_2 xs : List (α × β) n : Fin (length xs) ns : List (Fin (length xs)) hi : 0 < List.length (n :: ns) ⊢ List.get (List.map Prod.fst (nth xs n.val (_ : n.val < length xs) :: map (fun n => nth xs n.val (_ : n.val < length xs)) ns)) { val := 0, isLt := (_ : 0 < List.length (List.map Prod.fst (nths xs (n :: ns)))) } = List.get (List.map Prod.fst xs) { val := (List.get (n :: ns) { val := 0, isLt := hi }).val, isLt := (_ : (List.get (n :: ns) { val := 0, isLt := hi }).val < List.length (List.map Prod.fst xs)) }
η : Type u_η dec_η : DecidableEq η schema : Schema α : Type u_1 β : Type u_2 xs : List (α × β) n : Fin (length xs) ns : List (Fin (length xs)) hi : 0 < List.length (n :: ns) ⊢ List.get (List.map Prod.fst (List.get xs { val := n.val, isLt := (_ : n.val < List.length xs) } :: map (fun n => nth xs n.val (_ : n.val < length xs)) ns)) { val := 0, isLt := (_ : 0 < List.length (List.map Prod.fst (nths xs (n :: ns)))) } = List.get (List.map Prod.fst xs) { val := (List.get (n :: ns) { val := 0, isLt := hi }).val, isLt := (_ : (List.get (n :: ns) { val := 0, isLt := hi }).val < List.length (List.map Prod.fst xs)) }
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.get_map_nths_eq_get_get
[106, 1]
[126, 11]
simp only [List.get]
η : Type u_η dec_η : DecidableEq η schema : Schema α : Type u_1 β : Type u_2 xs : List (α × β) n : Fin (length xs) ns : List (Fin (length xs)) hi : 0 < List.length (n :: ns) ⊢ List.get (List.map Prod.fst (List.get xs { val := n.val, isLt := (_ : n.val < List.length xs) } :: map (fun n => nth xs n.val (_ : n.val < length xs)) ns)) { val := 0, isLt := (_ : 0 < List.length (List.map Prod.fst (nths xs (n :: ns)))) } = List.get (List.map Prod.fst xs) { val := (List.get (n :: ns) { val := 0, isLt := hi }).val, isLt := (_ : (List.get (n :: ns) { val := 0, isLt := hi }).val < List.length (List.map Prod.fst xs)) }
η : Type u_η dec_η : DecidableEq η schema : Schema α : Type u_1 β : Type u_2 xs : List (α × β) n : Fin (length xs) ns : List (Fin (length xs)) hi : 0 < List.length (n :: ns) ⊢ (List.get xs { val := n.val, isLt := (_ : n.val < List.length xs) }).fst = List.get (List.map Prod.fst xs) { val := n.val, isLt := (_ : n.val < List.length (List.map Prod.fst xs)) }
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.get_map_nths_eq_get_get
[106, 1]
[126, 11]
rw [List.get_map Prod.fst]
η : Type u_η dec_η : DecidableEq η schema : Schema α : Type u_1 β : Type u_2 xs : List (α × β) n : Fin (length xs) ns : List (Fin (length xs)) hi : 0 < List.length (n :: ns) ⊢ (List.get xs { val := n.val, isLt := (_ : n.val < List.length xs) }).fst = List.get (List.map Prod.fst xs) { val := n.val, isLt := (_ : n.val < List.length (List.map Prod.fst xs)) }
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.get_map_nths_eq_get_get
[106, 1]
[126, 11]
simp only [nths, map, get]
η : Type u_η dec_η : DecidableEq η schema : Schema α : Type u_1 β : Type u_2 xs : List (α × β) n : Fin (length xs) ns : List (Fin (length xs)) i : Nat hi : Nat.succ i < List.length (n :: ns) ⊢ List.get (List.map Prod.fst (nths xs (n :: ns))) { val := Nat.succ i, isLt := (_ : Nat.succ i < List.length (List.map Prod.fst (nths xs (n :: ns)))) } = List.get (List.map Prod.fst xs) { val := (List.get (n :: ns) { val := Nat.succ i, isLt := hi }).val, isLt := (_ : (List.get (n :: ns) { val := Nat.succ i, isLt := hi }).val < List.length (List.map Prod.fst xs)) }
η : Type u_η dec_η : DecidableEq η schema : Schema α : Type u_1 β : Type u_2 xs : List (α × β) n : Fin (length xs) ns : List (Fin (length xs)) i : Nat hi : Nat.succ i < List.length (n :: ns) ⊢ List.get (List.map Prod.fst (nth xs n.val (_ : n.val < length xs) :: map (fun n => nth xs n.val (_ : n.val < length xs)) ns)) { val := Nat.succ i, isLt := (_ : Nat.succ i < List.length (List.map Prod.fst (nths xs (n :: ns)))) } = List.get (List.map Prod.fst xs) { val := (List.get (n :: ns) { val := Nat.succ i, isLt := hi }).val, isLt := (_ : (List.get (n :: ns) { val := Nat.succ i, isLt := hi }).val < List.length (List.map Prod.fst xs)) }
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.get_map_nths_eq_get_get
[106, 1]
[126, 11]
have ih := get_map_nths_eq_get_get xs ns i (Nat.lt_of_succ_lt_succ hi)
η : Type u_η dec_η : DecidableEq η schema : Schema α : Type u_1 β : Type u_2 xs : List (α × β) n : Fin (length xs) ns : List (Fin (length xs)) i : Nat hi : Nat.succ i < List.length (n :: ns) ⊢ List.get (List.map Prod.fst (nth xs n.val (_ : n.val < length xs) :: map (fun n => nth xs n.val (_ : n.val < length xs)) ns)) { val := Nat.succ i, isLt := (_ : Nat.succ i < List.length (List.map Prod.fst (nths xs (n :: ns)))) } = List.get (List.map Prod.fst xs) { val := (List.get (n :: ns) { val := Nat.succ i, isLt := hi }).val, isLt := (_ : (List.get (n :: ns) { val := Nat.succ i, isLt := hi }).val < List.length (List.map Prod.fst xs)) }
η : Type u_η dec_η : DecidableEq η schema : Schema α : Type u_1 β : Type u_2 xs : List (α × β) n : Fin (length xs) ns : List (Fin (length xs)) i : Nat hi : Nat.succ i < List.length (n :: ns) ih : List.get (List.map Prod.fst (nths xs ns)) { val := i, isLt := (_ : i < List.length (List.map Prod.fst (nths xs ns))) } = List.get (List.map Prod.fst xs) { val := (List.get ns { val := i, isLt := (_ : i < List.length ns) }).val, isLt := (_ : (List.get ns { val := i, isLt := (_ : i < List.length ns) }).val < List.length (List.map Prod.fst xs)) } ⊢ List.get (List.map Prod.fst (nth xs n.val (_ : n.val < length xs) :: map (fun n => nth xs n.val (_ : n.val < length xs)) ns)) { val := Nat.succ i, isLt := (_ : Nat.succ i < List.length (List.map Prod.fst (nths xs (n :: ns)))) } = List.get (List.map Prod.fst xs) { val := (List.get (n :: ns) { val := Nat.succ i, isLt := hi }).val, isLt := (_ : (List.get (n :: ns) { val := Nat.succ i, isLt := hi }).val < List.length (List.map Prod.fst xs)) }
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.get_map_nths_eq_get_get
[106, 1]
[126, 11]
simp only [List.get]
η : Type u_η dec_η : DecidableEq η schema : Schema α : Type u_1 β : Type u_2 xs : List (α × β) n : Fin (length xs) ns : List (Fin (length xs)) i : Nat hi : Nat.succ i < List.length (n :: ns) ih : List.get (List.map Prod.fst (nths xs ns)) { val := i, isLt := (_ : i < List.length (List.map Prod.fst (nths xs ns))) } = List.get (List.map Prod.fst xs) { val := (List.get ns { val := i, isLt := (_ : i < List.length ns) }).val, isLt := (_ : (List.get ns { val := i, isLt := (_ : i < List.length ns) }).val < List.length (List.map Prod.fst xs)) } ⊢ List.get (List.map Prod.fst (nth xs n.val (_ : n.val < length xs) :: map (fun n => nth xs n.val (_ : n.val < length xs)) ns)) { val := Nat.succ i, isLt := (_ : Nat.succ i < List.length (List.map Prod.fst (nths xs (n :: ns)))) } = List.get (List.map Prod.fst xs) { val := (List.get (n :: ns) { val := Nat.succ i, isLt := hi }).val, isLt := (_ : (List.get (n :: ns) { val := Nat.succ i, isLt := hi }).val < List.length (List.map Prod.fst xs)) }
η : Type u_η dec_η : DecidableEq η schema : Schema α : Type u_1 β : Type u_2 xs : List (α × β) n : Fin (length xs) ns : List (Fin (length xs)) i : Nat hi : Nat.succ i < List.length (n :: ns) ih : List.get (List.map Prod.fst (nths xs ns)) { val := i, isLt := (_ : i < List.length (List.map Prod.fst (nths xs ns))) } = List.get (List.map Prod.fst xs) { val := (List.get ns { val := i, isLt := (_ : i < List.length ns) }).val, isLt := (_ : (List.get ns { val := i, isLt := (_ : i < List.length ns) }).val < List.length (List.map Prod.fst xs)) } ⊢ List.get (List.map Prod.fst (map (fun n => nth xs n.val (_ : n.val < length xs)) ns)) { val := i, isLt := (_ : Nat.succ i ≤ List.length (List.map Prod.fst (map (fun n => nth xs n.val (_ : n.val < length xs)) ns))) } = List.get (List.map Prod.fst xs) { val := (List.get ns { val := i, isLt := (_ : Nat.succ i ≤ List.length ns) }).val, isLt := (_ : (List.get ns { val := i, isLt := (_ : Nat.succ i ≤ List.length ns) }).val < List.length (List.map Prod.fst xs)) }
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.get_map_nths_eq_get_get
[106, 1]
[126, 11]
rw [←ih]
η : Type u_η dec_η : DecidableEq η schema : Schema α : Type u_1 β : Type u_2 xs : List (α × β) n : Fin (length xs) ns : List (Fin (length xs)) i : Nat hi : Nat.succ i < List.length (n :: ns) ih : List.get (List.map Prod.fst (nths xs ns)) { val := i, isLt := (_ : i < List.length (List.map Prod.fst (nths xs ns))) } = List.get (List.map Prod.fst xs) { val := (List.get ns { val := i, isLt := (_ : i < List.length ns) }).val, isLt := (_ : (List.get ns { val := i, isLt := (_ : i < List.length ns) }).val < List.length (List.map Prod.fst xs)) } ⊢ List.get (List.map Prod.fst (map (fun n => nth xs n.val (_ : n.val < length xs)) ns)) { val := i, isLt := (_ : Nat.succ i ≤ List.length (List.map Prod.fst (map (fun n => nth xs n.val (_ : n.val < length xs)) ns))) } = List.get (List.map Prod.fst xs) { val := (List.get ns { val := i, isLt := (_ : Nat.succ i ≤ List.length ns) }).val, isLt := (_ : (List.get ns { val := i, isLt := (_ : Nat.succ i ≤ List.length ns) }).val < List.length (List.map Prod.fst xs)) }
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.lookup_eq_lookup_append
[162, 1]
[173, 14]
intros s t c h
η : Type u_η dec_η : DecidableEq η schema : Schema ⊢ ∀ (s t : Schema) (c : η) (h : HasName c s), lookup s { fst := c, snd := h } = lookup (append s t) { fst := c, snd := hasNameOfAppend h }
η : Type u_η dec_η : DecidableEq η schema : Schema s t : Schema c : η h : HasName c s ⊢ lookup s { fst := c, snd := h } = lookup (append s t) { fst := c, snd := hasNameOfAppend h }
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.lookup_eq_lookup_append
[162, 1]
[173, 14]
induction h with | hd => simp only [Schema.hasNameOfAppend] rw [Schema.lookup_eq_1, Schema.lookup_eq_1] | tl h' ih => simp only [Schema.hasNameOfAppend] rw [Schema.lookup_eq_2, Schema.lookup_eq_2] exact ih
η : Type u_η dec_η : DecidableEq η schema : Schema s t : Schema c : η h : HasName c s ⊢ lookup s { fst := c, snd := h } = lookup (append s t) { fst := c, snd := hasNameOfAppend h }
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.lookup_eq_lookup_append
[162, 1]
[173, 14]
simp only [Schema.hasNameOfAppend]
case hd η : Type u_η dec_η : DecidableEq η schema : Schema s t : Schema c c✝ : η rs✝ : Schema τ✝ : Type u_1 ⊢ lookup ((c✝, τ✝) :: rs✝) { fst := c✝, snd := HasName.hd } = lookup (append ((c✝, τ✝) :: rs✝) t) { fst := c✝, snd := hasNameOfAppend HasName.hd }
case hd η : Type u_η dec_η : DecidableEq η schema : Schema s t : Schema c c✝ : η rs✝ : Schema τ✝ : Type u_1 ⊢ lookup ((c✝, τ✝) :: rs✝) { fst := c✝, snd := HasName.hd } = lookup (append ((c✝, τ✝) :: rs✝) t) { fst := c✝, snd := HasName.hd }
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.lookup_eq_lookup_append
[162, 1]
[173, 14]
rw [Schema.lookup_eq_1, Schema.lookup_eq_1]
case hd η : Type u_η dec_η : DecidableEq η schema : Schema s t : Schema c c✝ : η rs✝ : Schema τ✝ : Type u_1 ⊢ lookup ((c✝, τ✝) :: rs✝) { fst := c✝, snd := HasName.hd } = lookup (append ((c✝, τ✝) :: rs✝) t) { fst := c✝, snd := HasName.hd }
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.lookup_eq_lookup_append
[162, 1]
[173, 14]
simp only [Schema.hasNameOfAppend]
case tl η : Type u_η dec_η : DecidableEq η schema : Schema s t : Schema c : η r✝ : Header c✝ : η rs✝ : Schema h' : HasName c✝ rs✝ ih : lookup rs✝ { fst := c✝, snd := h' } = lookup (append rs✝ t) { fst := c✝, snd := hasNameOfAppend h' } ⊢ lookup (r✝ :: rs✝) { fst := c✝, snd := HasName.tl h' } = lookup (append (r✝ :: rs✝) t) { fst := c✝, snd := hasNameOfAppend (HasName.tl h') }
case tl η : Type u_η dec_η : DecidableEq η schema : Schema s t : Schema c : η r✝ : Header c✝ : η rs✝ : Schema h' : HasName c✝ rs✝ ih : lookup rs✝ { fst := c✝, snd := h' } = lookup (append rs✝ t) { fst := c✝, snd := hasNameOfAppend h' } ⊢ lookup (r✝ :: rs✝) { fst := c✝, snd := HasName.tl h' } = lookup (append (r✝ :: rs✝) t) { fst := c✝, snd := HasName.tl (hasNameOfAppend h') }
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.lookup_eq_lookup_append
[162, 1]
[173, 14]
rw [Schema.lookup_eq_2, Schema.lookup_eq_2]
case tl η : Type u_η dec_η : DecidableEq η schema : Schema s t : Schema c : η r✝ : Header c✝ : η rs✝ : Schema h' : HasName c✝ rs✝ ih : lookup rs✝ { fst := c✝, snd := h' } = lookup (append rs✝ t) { fst := c✝, snd := hasNameOfAppend h' } ⊢ lookup (r✝ :: rs✝) { fst := c✝, snd := HasName.tl h' } = lookup (append (r✝ :: rs✝) t) { fst := c✝, snd := HasName.tl (hasNameOfAppend h') }
case tl η : Type u_η dec_η : DecidableEq η schema : Schema s t : Schema c : η r✝ : Header c✝ : η rs✝ : Schema h' : HasName c✝ rs✝ ih : lookup rs✝ { fst := c✝, snd := h' } = lookup (append rs✝ t) { fst := c✝, snd := hasNameOfAppend h' } ⊢ lookup rs✝ { fst := c✝, snd := h' } = lookup (append rs✝ t) { fst := c✝, snd := hasNameOfAppend h' }
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.lookup_eq_lookup_append
[162, 1]
[173, 14]
exact ih
case tl η : Type u_η dec_η : DecidableEq η schema : Schema s t : Schema c : η r✝ : Header c✝ : η rs✝ : Schema h' : HasName c✝ rs✝ ih : lookup rs✝ { fst := c✝, snd := h' } = lookup (append rs✝ t) { fst := c✝, snd := hasNameOfAppend h' } ⊢ lookup rs✝ { fst := c✝, snd := h' } = lookup (append rs✝ t) { fst := c✝, snd := hasNameOfAppend h' }
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.mem_map_of_HasName
[176, 1]
[184, 13]
intro sch nm h
η : Type u_η dec_η : DecidableEq η schema : Schema ⊢ ∀ (sch : Schema) (nm : η), HasName nm sch → nm ∈ map Prod.fst sch
η : Type u_η dec_η : DecidableEq η schema : Schema sch : Schema nm : η h : HasName nm sch ⊢ nm ∈ map Prod.fst sch
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.mem_map_of_HasName
[176, 1]
[184, 13]
induction h with | hd => apply List.Mem.head | tl _ ih => apply List.Mem.tail apply ih
η : Type u_η dec_η : DecidableEq η schema : Schema sch : Schema nm : η h : HasName nm sch ⊢ nm ∈ map Prod.fst sch
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.mem_map_of_HasName
[176, 1]
[184, 13]
apply List.Mem.head
case hd η : Type u_η dec_η : DecidableEq η schema : Schema sch : Schema nm c✝ : η rs✝ : Schema τ✝ : Type u_1 ⊢ c✝ ∈ map Prod.fst ((c✝, τ✝) :: rs✝)
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.mem_map_of_HasName
[176, 1]
[184, 13]
apply List.Mem.tail
case tl η : Type u_η dec_η : DecidableEq η schema : Schema sch : Schema nm : η r✝ : Header c✝ : η rs✝ : Schema a✝ : HasName c✝ rs✝ ih : c✝ ∈ map Prod.fst rs✝ ⊢ c✝ ∈ map Prod.fst (r✝ :: rs✝)
case tl.a η : Type u_η dec_η : DecidableEq η schema : Schema sch : Schema nm : η r✝ : Header c✝ : η rs✝ : Schema a✝ : HasName c✝ rs✝ ih : c✝ ∈ map Prod.fst rs✝ ⊢ List.Mem c✝ (map Prod.fst rs✝)
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.mem_map_of_HasName
[176, 1]
[184, 13]
apply ih
case tl.a η : Type u_η dec_η : DecidableEq η schema : Schema sch : Schema nm : η r✝ : Header c✝ : η rs✝ : Schema a✝ : HasName c✝ rs✝ ih : c✝ ∈ map Prod.fst rs✝ ⊢ List.Mem c✝ (map Prod.fst rs✝)
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.retypedFromSubschema_preserves_names
[228, 1]
[239, 79]
simp only [retypedFromSubschema]
η : Type u_η dec_η : DecidableEq η schema : Schema fst✝ : η snd✝ : Type u_1 ss : List Header nm : η τ : Type u_1 pf : HasName (nm, τ).fst ((fst✝, snd✝) :: ss) rs : List ((h : Header) × HasName h.fst ((fst✝, snd✝) :: ss)) ⊢ names (retypedFromSubschema ({ fst := (nm, τ), snd := pf } :: rs)) = names ((fst✝, snd✝) :: ss)
η : Type u_η dec_η : DecidableEq η schema : Schema fst✝ : η snd✝ : Type u_1 ss : List Header nm : η τ : Type u_1 pf : HasName (nm, τ).fst ((fst✝, snd✝) :: ss) rs : List ((h : Header) × HasName h.fst ((fst✝, snd✝) :: ss)) ⊢ names (retypedFromSubschema (map (fun x => { fst := x.fst, snd := hasRetypedName x.snd }) rs)) = names ((fst✝, snd✝) :: ss)
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.retypedFromSubschema_preserves_names
[228, 1]
[239, 79]
have := retypedFromSubschema_preserves_names (Schema.retypeColumn _ pf τ) (Schema.map (fun ⟨h, pf⟩ => ⟨h, hasRetypedName pf⟩) rs)
η : Type u_η dec_η : DecidableEq η schema : Schema fst✝ : η snd✝ : Type u_1 ss : List Header nm : η τ : Type u_1 pf : HasName (nm, τ).fst ((fst✝, snd✝) :: ss) rs : List ((h : Header) × HasName h.fst ((fst✝, snd✝) :: ss)) ⊢ names (retypedFromSubschema (map (fun x => { fst := x.fst, snd := hasRetypedName x.snd }) rs)) = names ((fst✝, snd✝) :: ss)
η : Type u_η dec_η : DecidableEq η schema : Schema fst✝ : η snd✝ : Type u_1 ss : List Header nm : η τ : Type u_1 pf : HasName (nm, τ).fst ((fst✝, snd✝) :: ss) rs : List ((h : Header) × HasName h.fst ((fst✝, snd✝) :: ss)) this : names (retypedFromSubschema (map (fun x => match x with | { fst := h, snd := pf_1 } => { fst := h, snd := hasRetypedName pf_1 }) rs)) = names (retypeColumn ((fst✝, snd✝) :: ss) pf τ) ⊢ names (retypedFromSubschema (map (fun x => { fst := x.fst, snd := hasRetypedName x.snd }) rs)) = names ((fst✝, snd✝) :: ss)
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.retypedFromSubschema_preserves_names
[228, 1]
[239, 79]
rw [this]
η : Type u_η dec_η : DecidableEq η schema : Schema fst✝ : η snd✝ : Type u_1 ss : List Header nm : η τ : Type u_1 pf : HasName (nm, τ).fst ((fst✝, snd✝) :: ss) rs : List ((h : Header) × HasName h.fst ((fst✝, snd✝) :: ss)) this : names (retypedFromSubschema (map (fun x => match x with | { fst := h, snd := pf_1 } => { fst := h, snd := hasRetypedName pf_1 }) rs)) = names (retypeColumn ((fst✝, snd✝) :: ss) pf τ) ⊢ names (retypedFromSubschema (map (fun x => { fst := x.fst, snd := hasRetypedName x.snd }) rs)) = names ((fst✝, snd✝) :: ss)
η : Type u_η dec_η : DecidableEq η schema : Schema fst✝ : η snd✝ : Type u_1 ss : List Header nm : η τ : Type u_1 pf : HasName (nm, τ).fst ((fst✝, snd✝) :: ss) rs : List ((h : Header) × HasName h.fst ((fst✝, snd✝) :: ss)) this : names (retypedFromSubschema (map (fun x => match x with | { fst := h, snd := pf_1 } => { fst := h, snd := hasRetypedName pf_1 }) rs)) = names (retypeColumn ((fst✝, snd✝) :: ss) pf τ) ⊢ names (retypeColumn ((fst✝, snd✝) :: ss) pf τ) = names ((fst✝, snd✝) :: ss)
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.retypedFromSubschema_preserves_names
[228, 1]
[239, 79]
simp only [retypeColumn_preserves_names]
η : Type u_η dec_η : DecidableEq η schema : Schema fst✝ : η snd✝ : Type u_1 ss : List Header nm : η τ : Type u_1 pf : HasName (nm, τ).fst ((fst✝, snd✝) :: ss) rs : List ((h : Header) × HasName h.fst ((fst✝, snd✝) :: ss)) this : names (retypedFromSubschema (map (fun x => match x with | { fst := h, snd := pf_1 } => { fst := h, snd := hasRetypedName pf_1 }) rs)) = names (retypeColumn ((fst✝, snd✝) :: ss) pf τ) ⊢ names (retypeColumn ((fst✝, snd✝) :: ss) pf τ) = names ((fst✝, snd✝) :: ss)
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.hasNameOfFromCHeaders_eq_1
[263, 1]
[268, 46]
cases sch with | nil => contradiction | cons s ss => simp [hasNameOfFromCHeaders]
η : Type u_η dec_η : DecidableEq η schema : Schema sch : Schema nm : η τ : Type u_1 hpf : HasCol (nm, τ) sch cs : List (CertifiedHeader sch) ⊢ hasNameOfFromCHeaders HasName.hd = colImpliesName hpf
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.hasNameOfFromCHeaders_eq_1
[263, 1]
[268, 46]
contradiction
case nil η : Type u_η dec_η : DecidableEq η schema : Schema nm : η τ : Type u_1 hpf : HasCol (nm, τ) [] cs : List (CertifiedHeader []) ⊢ hasNameOfFromCHeaders HasName.hd = colImpliesName hpf
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.hasNameOfFromCHeaders_eq_1
[263, 1]
[268, 46]
simp [hasNameOfFromCHeaders]
case cons η : Type u_η dec_η : DecidableEq η schema : Schema nm : η τ : Type u_1 s : Header ss : List Header hpf : HasCol (nm, τ) (s :: ss) cs : List (CertifiedHeader (s :: ss)) ⊢ hasNameOfFromCHeaders HasName.hd = colImpliesName hpf
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.hasNameOfFromCHeaders_eq_2
[270, 1]
[275, 46]
cases sch with | nil => contradiction | cons s ss => simp [hasNameOfFromCHeaders]
η : Type u_η dec_η : DecidableEq η schema : Schema sch : Schema hdr : Header hpf : HasCol hdr sch cs : List (CertifiedHeader sch) nm : η h : HasName nm (map Sigma.fst cs) ⊢ hasNameOfFromCHeaders (HasName.tl h) = hasNameOfFromCHeaders h
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.hasNameOfFromCHeaders_eq_2
[270, 1]
[275, 46]
contradiction
case nil η : Type u_η dec_η : DecidableEq η schema : Schema hdr : Header nm : η hpf : HasCol hdr [] cs : List (CertifiedHeader []) h : HasName nm (map Sigma.fst cs) ⊢ hasNameOfFromCHeaders (HasName.tl h) = hasNameOfFromCHeaders h
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.hasNameOfFromCHeaders_eq_2
[270, 1]
[275, 46]
simp [hasNameOfFromCHeaders]
case cons η : Type u_η dec_η : DecidableEq η schema : Schema hdr : Header nm : η s : Header ss : List Header hpf : HasCol hdr (s :: ss) cs : List (CertifiedHeader (s :: ss)) h : HasName nm (map Sigma.fst cs) ⊢ hasNameOfFromCHeaders (HasName.tl h) = hasNameOfFromCHeaders h
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.lookupTypeFromCHeadersUnique
[290, 1]
[311, 51]
simp only [lookupType]
η : Type u_η dec_η : DecidableEq η schema : Schema nm : η τ : Type u_1 hs : List Header cs : List (CertifiedHeader ((nm, τ) :: hs)) ⊢ lookupType ((nm, τ) :: hs) { fst := { fst := nm, snd := HasName.hd }.fst, snd := hasNameOfFromCHeaders { fst := nm, snd := HasName.hd }.snd } = lookupType (fromCHeaders ({ fst := (nm, τ), snd := HasCol.hd } :: cs)) { fst := nm, snd := HasName.hd }
η : Type u_η dec_η : DecidableEq η schema : Schema nm : η τ : Type u_1 hs : List Header cs : List (CertifiedHeader ((nm, τ) :: hs)) ⊢ lookupType ((nm, τ) :: hs) { fst := nm, snd := hasNameOfFromCHeaders HasName.hd } = τ
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.lookupTypeFromCHeadersUnique
[290, 1]
[311, 51]
simp only [hasNameOfFromCHeaders_eq_1]
η : Type u_η dec_η : DecidableEq η schema : Schema nm : η τ : Type u_1 hs : List Header cs : List (CertifiedHeader ((nm, τ) :: hs)) ⊢ lookupType ((nm, τ) :: hs) { fst := nm, snd := hasNameOfFromCHeaders HasName.hd } = τ
η : Type u_η dec_η : DecidableEq η schema : Schema nm : η τ : Type u_1 hs : List Header cs : List (CertifiedHeader ((nm, τ) :: hs)) ⊢ lookupType ((nm, τ) :: hs) { fst := nm, snd := colImpliesName HasCol.hd } = τ
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.lookupTypeFromCHeadersUnique
[290, 1]
[311, 51]
rw [@colImpliesName_eq_1 η hs (nm, τ)]
η : Type u_η dec_η : DecidableEq η schema : Schema nm : η τ : Type u_1 hs : List Header cs : List (CertifiedHeader ((nm, τ) :: hs)) ⊢ lookupType ((nm, τ) :: hs) { fst := nm, snd := colImpliesName HasCol.hd } = τ
η : Type u_η dec_η : DecidableEq η schema : Schema nm : η τ : Type u_1 hs : List Header cs : List (CertifiedHeader ((nm, τ) :: hs)) ⊢ lookupType ((nm, τ) :: hs) { fst := nm, snd := HasName.hd } = τ
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.lookupTypeFromCHeadersUnique
[290, 1]
[311, 51]
simp only [lookupType]
η : Type u_η dec_η : DecidableEq η schema : Schema nm : η τ : Type u_1 hs : List Header cs : List (CertifiedHeader ((nm, τ) :: hs)) ⊢ lookupType ((nm, τ) :: hs) { fst := nm, snd := HasName.hd } = τ
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.lookupTypeFromCHeadersUnique
[290, 1]
[311, 51]
simp only [lookupType]
η : Type u_η dec_η : DecidableEq η schema : Schema nm : η τ : Type u_1 hs : List Header ch_nm : η ch_τ : Type u_1 h : HasCol (ch_nm, ch_τ) hs cs : List (CertifiedHeader ((nm, τ) :: hs)) ⊢ lookupType ((nm, τ) :: hs) { fst := { fst := ch_nm, snd := HasName.hd }.fst, snd := hasNameOfFromCHeaders { fst := ch_nm, snd := HasName.hd }.snd } = lookupType (fromCHeaders ({ fst := (ch_nm, ch_τ), snd := HasCol.tl h } :: cs)) { fst := ch_nm, snd := HasName.hd }
η : Type u_η dec_η : DecidableEq η schema : Schema nm : η τ : Type u_1 hs : List Header ch_nm : η ch_τ : Type u_1 h : HasCol (ch_nm, ch_τ) hs cs : List (CertifiedHeader ((nm, τ) :: hs)) ⊢ lookupType ((nm, τ) :: hs) { fst := ch_nm, snd := hasNameOfFromCHeaders HasName.hd } = ch_τ
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.lookupTypeFromCHeadersUnique
[290, 1]
[311, 51]
simp only [hasNameOfFromCHeaders_eq_1]
η : Type u_η dec_η : DecidableEq η schema : Schema nm : η τ : Type u_1 hs : List Header ch_nm : η ch_τ : Type u_1 h : HasCol (ch_nm, ch_τ) hs cs : List (CertifiedHeader ((nm, τ) :: hs)) ⊢ lookupType ((nm, τ) :: hs) { fst := ch_nm, snd := hasNameOfFromCHeaders HasName.hd } = ch_τ
η : Type u_η dec_η : DecidableEq η schema : Schema nm : η τ : Type u_1 hs : List Header ch_nm : η ch_τ : Type u_1 h : HasCol (ch_nm, ch_τ) hs cs : List (CertifiedHeader ((nm, τ) :: hs)) ⊢ lookupType ((nm, τ) :: hs) { fst := ch_nm, snd := colImpliesName (HasCol.tl h) } = ch_τ
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.lookupTypeFromCHeadersUnique
[290, 1]
[311, 51]
rw [@colImpliesName_eq_2 η hs (nm, τ) (ch_nm, ch_τ) h]
η : Type u_η dec_η : DecidableEq η schema : Schema nm : η τ : Type u_1 hs : List Header ch_nm : η ch_τ : Type u_1 h : HasCol (ch_nm, ch_τ) hs cs : List (CertifiedHeader ((nm, τ) :: hs)) ⊢ lookupType ((nm, τ) :: hs) { fst := ch_nm, snd := colImpliesName (HasCol.tl h) } = ch_τ
η : Type u_η dec_η : DecidableEq η schema : Schema nm : η τ : Type u_1 hs : List Header ch_nm : η ch_τ : Type u_1 h : HasCol (ch_nm, ch_τ) hs cs : List (CertifiedHeader ((nm, τ) :: hs)) ⊢ lookupType ((nm, τ) :: hs) { fst := ch_nm, snd := HasName.tl (colImpliesName h) } = ch_τ
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.lookupTypeFromCHeadersUnique
[290, 1]
[311, 51]
simp only [lookupType]
η : Type u_η dec_η : DecidableEq η schema : Schema nm : η τ : Type u_1 hs : List Header ch_nm : η ch_τ : Type u_1 h : HasCol (ch_nm, ch_τ) hs cs : List (CertifiedHeader ((nm, τ) :: hs)) ⊢ lookupType ((nm, τ) :: hs) { fst := ch_nm, snd := HasName.tl (colImpliesName h) } = ch_τ
η : Type u_η dec_η : DecidableEq η schema : Schema nm : η τ : Type u_1 hs : List Header ch_nm : η ch_τ : Type u_1 h : HasCol (ch_nm, ch_τ) hs cs : List (CertifiedHeader ((nm, τ) :: hs)) ⊢ lookupType hs { fst := ch_nm, snd := colImpliesName h } = ch_τ
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.lookupTypeFromCHeadersUnique
[290, 1]
[311, 51]
apply lookupType_of_colImpliesName
η : Type u_η dec_η : DecidableEq η schema : Schema nm : η τ : Type u_1 hs : List Header ch_nm : η ch_τ : Type u_1 h : HasCol (ch_nm, ch_τ) hs cs : List (CertifiedHeader ((nm, τ) :: hs)) ⊢ lookupType hs { fst := ch_nm, snd := colImpliesName h } = ch_τ
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.lookupTypeFromCHeadersUnique
[290, 1]
[311, 51]
simp only [lookupType]
η : Type u_η dec_η : DecidableEq η schema : Schema nm : η τ : Type u_1 hs : List Header fst✝ : Header pf : HasCol fst✝ ((nm, τ) :: hs) cs : List (CertifiedHeader ((nm, τ) :: hs)) s_nm : η hn : HasName s_nm (map Sigma.fst cs) ⊢ lookupType ((nm, τ) :: hs) { fst := { fst := s_nm, snd := HasName.tl hn }.fst, snd := hasNameOfFromCHeaders { fst := s_nm, snd := HasName.tl hn }.snd } = lookupType (fromCHeaders ({ fst := fst✝, snd := pf } :: cs)) { fst := s_nm, snd := HasName.tl hn }
η : Type u_η dec_η : DecidableEq η schema : Schema nm : η τ : Type u_1 hs : List Header fst✝ : Header pf : HasCol fst✝ ((nm, τ) :: hs) cs : List (CertifiedHeader ((nm, τ) :: hs)) s_nm : η hn : HasName s_nm (map Sigma.fst cs) ⊢ lookupType ((nm, τ) :: hs) { fst := s_nm, snd := hasNameOfFromCHeaders (HasName.tl hn) } = lookupType (map Sigma.fst cs) { fst := s_nm, snd := hn }
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.lookupTypeFromCHeadersUnique
[290, 1]
[311, 51]
simp only [hasNameOfFromCHeaders_eq_2]
η : Type u_η dec_η : DecidableEq η schema : Schema nm : η τ : Type u_1 hs : List Header fst✝ : Header pf : HasCol fst✝ ((nm, τ) :: hs) cs : List (CertifiedHeader ((nm, τ) :: hs)) s_nm : η hn : HasName s_nm (map Sigma.fst cs) ⊢ lookupType ((nm, τ) :: hs) { fst := s_nm, snd := hasNameOfFromCHeaders (HasName.tl hn) } = lookupType (map Sigma.fst cs) { fst := s_nm, snd := hn }
η : Type u_η dec_η : DecidableEq η schema : Schema nm : η τ : Type u_1 hs : List Header fst✝ : Header pf : HasCol fst✝ ((nm, τ) :: hs) cs : List (CertifiedHeader ((nm, τ) :: hs)) s_nm : η hn : HasName s_nm (map Sigma.fst cs) ⊢ lookupType ((nm, τ) :: hs) { fst := s_nm, snd := hasNameOfFromCHeaders hn } = lookupType (map Sigma.fst cs) { fst := s_nm, snd := hn }
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.lookupTypeFromCHeadersUnique
[290, 1]
[311, 51]
exact lookupTypeFromCHeadersUnique cs ⟨s_nm, hn⟩
η : Type u_η dec_η : DecidableEq η schema : Schema nm : η τ : Type u_1 hs : List Header fst✝ : Header pf : HasCol fst✝ ((nm, τ) :: hs) cs : List (CertifiedHeader ((nm, τ) :: hs)) s_nm : η hn : HasName s_nm (map Sigma.fst cs) ⊢ lookupType ((nm, τ) :: hs) { fst := s_nm, snd := hasNameOfFromCHeaders hn } = lookupType (map Sigma.fst cs) { fst := s_nm, snd := hn }
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.hasNameEqHeadOrTail_inl
[352, 1]
[358, 18]
intro eqt
η : Type u_η dec_η : DecidableEq η schema : Schema η✝ : Type u_1 nm : η✝ τ : Type u_2 hs : List Header h : HasName nm ((nm, τ) :: hs) ⊢ hasNameEqHeadOrTail h ≡ Sum.inl (EqT.refl nm) → h = HasName.hd
η : Type u_η dec_η : DecidableEq η schema : Schema η✝ : Type u_1 nm : η✝ τ : Type u_2 hs : List Header h : HasName nm ((nm, τ) :: hs) eqt : hasNameEqHeadOrTail h ≡ Sum.inl (EqT.refl nm) ⊢ h = HasName.hd
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.hasNameEqHeadOrTail_inl
[352, 1]
[358, 18]
simp only [hasNameEqHeadOrTail] at eqt
η : Type u_η dec_η : DecidableEq η schema : Schema η✝ : Type u_1 nm : η✝ τ : Type u_2 hs : List Header h : HasName nm ((nm, τ) :: hs) eqt : hasNameEqHeadOrTail h ≡ Sum.inl (EqT.refl nm) ⊢ h = HasName.hd
η : Type u_η dec_η : DecidableEq η schema : Schema η✝ : Type u_1 nm : η✝ τ : Type u_2 hs : List Header h : HasName nm ((nm, τ) :: hs) eqt : (match nm, hs, h with | .(nm), x, HasName.hd => Sum.inl (EqT.refl nm) | x, x_1, HasName.tl htl => Sum.inr htl) ≡ Sum.inl (EqT.refl nm) ⊢ h = HasName.hd
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.hasNameEqHeadOrTail_inl
[352, 1]
[358, 18]
cases h
η : Type u_η dec_η : DecidableEq η schema : Schema η✝ : Type u_1 nm : η✝ τ : Type u_2 hs : List Header h : HasName nm ((nm, τ) :: hs) eqt : (match nm, hs, h with | .(nm), x, HasName.hd => Sum.inl (EqT.refl nm) | x, x_1, HasName.tl htl => Sum.inr htl) ≡ Sum.inl (EqT.refl nm) ⊢ h = HasName.hd
case hd η : Type u_η dec_η : DecidableEq η schema : Schema η✝ : Type u_1 nm : η✝ τ : Type u_2 hs : List Header eqt : (match nm, hs, HasName.hd with | .(nm), x, HasName.hd => Sum.inl (EqT.refl nm) | x, x_1, HasName.tl htl => Sum.inr htl) ≡ Sum.inl (EqT.refl nm) ⊢ HasName.hd = HasName.hd case tl η : Type u_η dec_η : DecidableEq η schema : Schema η✝ : Type u_1 nm : η✝ τ : Type u_2 hs : List Header a✝ : HasName nm hs eqt : (match nm, hs, HasName.tl a✝ with | .(nm), x, HasName.hd => Sum.inl (EqT.refl nm) | x, x_1, HasName.tl htl => Sum.inr htl) ≡ Sum.inl (EqT.refl nm) ⊢ HasName.tl a✝ = HasName.hd
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.hasNameEqHeadOrTail_inl
[352, 1]
[358, 18]
. rfl
case hd η : Type u_η dec_η : DecidableEq η schema : Schema η✝ : Type u_1 nm : η✝ τ : Type u_2 hs : List Header eqt : (match nm, hs, HasName.hd with | .(nm), x, HasName.hd => Sum.inl (EqT.refl nm) | x, x_1, HasName.tl htl => Sum.inr htl) ≡ Sum.inl (EqT.refl nm) ⊢ HasName.hd = HasName.hd case tl η : Type u_η dec_η : DecidableEq η schema : Schema η✝ : Type u_1 nm : η✝ τ : Type u_2 hs : List Header a✝ : HasName nm hs eqt : (match nm, hs, HasName.tl a✝ with | .(nm), x, HasName.hd => Sum.inl (EqT.refl nm) | x, x_1, HasName.tl htl => Sum.inr htl) ≡ Sum.inl (EqT.refl nm) ⊢ HasName.tl a✝ = HasName.hd
case tl η : Type u_η dec_η : DecidableEq η schema : Schema η✝ : Type u_1 nm : η✝ τ : Type u_2 hs : List Header a✝ : HasName nm hs eqt : (match nm, hs, HasName.tl a✝ with | .(nm), x, HasName.hd => Sum.inl (EqT.refl nm) | x, x_1, HasName.tl htl => Sum.inr htl) ≡ Sum.inl (EqT.refl nm) ⊢ HasName.tl a✝ = HasName.hd
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.hasNameEqHeadOrTail_inl
[352, 1]
[358, 18]
. contradiction
case tl η : Type u_η dec_η : DecidableEq η schema : Schema η✝ : Type u_1 nm : η✝ τ : Type u_2 hs : List Header a✝ : HasName nm hs eqt : (match nm, hs, HasName.tl a✝ with | .(nm), x, HasName.hd => Sum.inl (EqT.refl nm) | x, x_1, HasName.tl htl => Sum.inr htl) ≡ Sum.inl (EqT.refl nm) ⊢ HasName.tl a✝ = HasName.hd
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.hasNameEqHeadOrTail_inl
[352, 1]
[358, 18]
rfl
case hd η : Type u_η dec_η : DecidableEq η schema : Schema η✝ : Type u_1 nm : η✝ τ : Type u_2 hs : List Header eqt : (match nm, hs, HasName.hd with | .(nm), x, HasName.hd => Sum.inl (EqT.refl nm) | x, x_1, HasName.tl htl => Sum.inr htl) ≡ Sum.inl (EqT.refl nm) ⊢ HasName.hd = HasName.hd
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.hasNameEqHeadOrTail_inl
[352, 1]
[358, 18]
contradiction
case tl η : Type u_η dec_η : DecidableEq η schema : Schema η✝ : Type u_1 nm : η✝ τ : Type u_2 hs : List Header a✝ : HasName nm hs eqt : (match nm, hs, HasName.tl a✝ with | .(nm), x, HasName.hd => Sum.inl (EqT.refl nm) | x, x_1, HasName.tl htl => Sum.inr htl) ≡ Sum.inl (EqT.refl nm) ⊢ HasName.tl a✝ = HasName.hd
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.hasNameEqHeadOrTail_inr
[360, 1]
[370, 8]
intro eqt
η : Type u_η dec_η : DecidableEq η schema : Schema η✝ : Type u_1 nm : η✝ h✝ : Header hs : List Header h : HasName nm (h✝ :: hs) htl : HasName nm hs ⊢ hasNameEqHeadOrTail h ≡ Sum.inr htl → h = HasName.tl htl
η : Type u_η dec_η : DecidableEq η schema : Schema η✝ : Type u_1 nm : η✝ h✝ : Header hs : List Header h : HasName nm (h✝ :: hs) htl : HasName nm hs eqt : hasNameEqHeadOrTail h ≡ Sum.inr htl ⊢ h = HasName.tl htl
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.hasNameEqHeadOrTail_inr
[360, 1]
[370, 8]
simp only [hasNameEqHeadOrTail] at eqt
η : Type u_η dec_η : DecidableEq η schema : Schema η✝ : Type u_1 nm : η✝ h✝ : Header hs : List Header h : HasName nm (h✝ :: hs) htl : HasName nm hs eqt : hasNameEqHeadOrTail h ≡ Sum.inr htl ⊢ h = HasName.tl htl
η : Type u_η dec_η : DecidableEq η schema : Schema η✝ : Type u_1 nm : η✝ h✝ : Header hs : List Header h : HasName nm (h✝ :: hs) htl : HasName nm hs eqt : (match nm, hs, h with | .(h✝.fst), x, HasName.hd => Sum.inl (EqT.refl h✝.fst) | x, x_1, HasName.tl htl => Sum.inr htl) ≡ Sum.inr htl ⊢ h = HasName.tl htl
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.hasNameEqHeadOrTail_inr
[360, 1]
[370, 8]
cases h
η : Type u_η dec_η : DecidableEq η schema : Schema η✝ : Type u_1 nm : η✝ h✝ : Header hs : List Header h : HasName nm (h✝ :: hs) htl : HasName nm hs eqt : (match nm, hs, h with | .(h✝.fst), x, HasName.hd => Sum.inl (EqT.refl h✝.fst) | x, x_1, HasName.tl htl => Sum.inr htl) ≡ Sum.inr htl ⊢ h = HasName.tl htl
case hd η : Type u_η dec_η : DecidableEq η schema : Schema η✝ : Type u_1 nm : η✝ hs : List Header htl : HasName nm hs τ✝ : Type u_2 eqt : (match nm, hs, HasName.hd with | .((nm, τ✝).fst), x, HasName.hd => Sum.inl (EqT.refl (nm, τ✝).fst) | x, x_1, HasName.tl htl => Sum.inr htl) ≡ Sum.inr htl ⊢ HasName.hd = HasName.tl htl case tl η : Type u_η dec_η : DecidableEq η schema : Schema η✝ : Type u_1 nm : η✝ h : Header hs : List Header htl a✝ : HasName nm hs eqt : (match nm, hs, HasName.tl a✝ with | .(h.fst), x, HasName.hd => Sum.inl (EqT.refl h.fst) | x, x_1, HasName.tl htl => Sum.inr htl) ≡ Sum.inr htl ⊢ HasName.tl a✝ = HasName.tl htl
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.hasNameEqHeadOrTail_inr
[360, 1]
[370, 8]
. contradiction
case hd η : Type u_η dec_η : DecidableEq η schema : Schema η✝ : Type u_1 nm : η✝ hs : List Header htl : HasName nm hs τ✝ : Type u_2 eqt : (match nm, hs, HasName.hd with | .((nm, τ✝).fst), x, HasName.hd => Sum.inl (EqT.refl (nm, τ✝).fst) | x, x_1, HasName.tl htl => Sum.inr htl) ≡ Sum.inr htl ⊢ HasName.hd = HasName.tl htl case tl η : Type u_η dec_η : DecidableEq η schema : Schema η✝ : Type u_1 nm : η✝ h : Header hs : List Header htl a✝ : HasName nm hs eqt : (match nm, hs, HasName.tl a✝ with | .(h.fst), x, HasName.hd => Sum.inl (EqT.refl h.fst) | x, x_1, HasName.tl htl => Sum.inr htl) ≡ Sum.inr htl ⊢ HasName.tl a✝ = HasName.tl htl
case tl η : Type u_η dec_η : DecidableEq η schema : Schema η✝ : Type u_1 nm : η✝ h : Header hs : List Header htl a✝ : HasName nm hs eqt : (match nm, hs, HasName.tl a✝ with | .(h.fst), x, HasName.hd => Sum.inl (EqT.refl h.fst) | x, x_1, HasName.tl htl => Sum.inr htl) ≡ Sum.inr htl ⊢ HasName.tl a✝ = HasName.tl htl
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.hasNameEqHeadOrTail_inr
[360, 1]
[370, 8]
. simp only at eqt cases eqt rfl
case tl η : Type u_η dec_η : DecidableEq η schema : Schema η✝ : Type u_1 nm : η✝ h : Header hs : List Header htl a✝ : HasName nm hs eqt : (match nm, hs, HasName.tl a✝ with | .(h.fst), x, HasName.hd => Sum.inl (EqT.refl h.fst) | x, x_1, HasName.tl htl => Sum.inr htl) ≡ Sum.inr htl ⊢ HasName.tl a✝ = HasName.tl htl
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.hasNameEqHeadOrTail_inr
[360, 1]
[370, 8]
contradiction
case hd η : Type u_η dec_η : DecidableEq η schema : Schema η✝ : Type u_1 nm : η✝ hs : List Header htl : HasName nm hs τ✝ : Type u_2 eqt : (match nm, hs, HasName.hd with | .((nm, τ✝).fst), x, HasName.hd => Sum.inl (EqT.refl (nm, τ✝).fst) | x, x_1, HasName.tl htl => Sum.inr htl) ≡ Sum.inr htl ⊢ HasName.hd = HasName.tl htl
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.hasNameEqHeadOrTail_inr
[360, 1]
[370, 8]
simp only at eqt
case tl η : Type u_η dec_η : DecidableEq η schema : Schema η✝ : Type u_1 nm : η✝ h : Header hs : List Header htl a✝ : HasName nm hs eqt : (match nm, hs, HasName.tl a✝ with | .(h.fst), x, HasName.hd => Sum.inl (EqT.refl h.fst) | x, x_1, HasName.tl htl => Sum.inr htl) ≡ Sum.inr htl ⊢ HasName.tl a✝ = HasName.tl htl
case tl η : Type u_η dec_η : DecidableEq η schema : Schema η✝ : Type u_1 nm : η✝ h : Header hs : List Header htl a✝ : HasName nm hs eqt : Sum.inr a✝ ≡ Sum.inr htl ⊢ HasName.tl a✝ = HasName.tl htl
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.hasNameEqHeadOrTail_inr
[360, 1]
[370, 8]
cases eqt
case tl η : Type u_η dec_η : DecidableEq η schema : Schema η✝ : Type u_1 nm : η✝ h : Header hs : List Header htl a✝ : HasName nm hs eqt : Sum.inr a✝ ≡ Sum.inr htl ⊢ HasName.tl a✝ = HasName.tl htl
case tl.refl η : Type u_η dec_η : DecidableEq η schema : Schema η✝ : Type u_1 nm : η✝ h : Header hs : List Header htl : HasName nm hs ⊢ HasName.tl htl = HasName.tl htl
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.hasNameEqHeadOrTail_inr
[360, 1]
[370, 8]
rfl
case tl.refl η : Type u_η dec_η : DecidableEq η schema : Schema η✝ : Type u_1 nm : η✝ h : Header hs : List Header htl : HasName nm hs ⊢ HasName.tl htl = HasName.tl htl
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.lookupType_nths_eq_lookupType
[372, 1]
[413, 28]
simp only [Schema.lookupType]
η : Type u_η dec_η : DecidableEq η schema : Schema snm : η sτ : Type u_1 sch : List Header hlt : 0 < length ((snm, sτ) :: sch) ns : List (Fin (length ((snm, sτ) :: sch))) ⊢ lookupType (nths ((snm, sτ) :: sch) ({ val := 0, isLt := hlt } :: ns)) { fst := snm, snd := HasName.hd } = lookupType ((snm, sτ) :: sch) { fst := snm, snd := hasNameOfNthsHasName HasName.hd }
η : Type u_η dec_η : DecidableEq η schema : Schema snm : η sτ : Type u_1 sch : List Header hlt : 0 < length ((snm, sτ) :: sch) ns : List (Fin (length ((snm, sτ) :: sch))) ⊢ sτ = lookupType ((snm, sτ) :: sch) { fst := snm, snd := hasNameOfNthsHasName HasName.hd }
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.lookupType_nths_eq_lookupType
[372, 1]
[413, 28]
unfold Schema.hasNameOfNthsHasName
η : Type u_η dec_η : DecidableEq η schema : Schema snm : η sτ : Type u_1 sch : List Header hlt : 0 < length ((snm, sτ) :: sch) ns : List (Fin (length ((snm, sτ) :: sch))) ⊢ sτ = lookupType ((snm, sτ) :: sch) { fst := snm, snd := hasNameOfNthsHasName HasName.hd }
η : Type u_η dec_η : DecidableEq η schema : Schema snm : η sτ : Type u_1 sch : List Header hlt : 0 < length ((snm, sτ) :: sch) ns : List (Fin (length ((snm, sτ) :: sch))) ⊢ sτ = lookupType ((snm, sτ) :: sch) { fst := snm, snd := match snm, hasNameEqHeadOrTail HasName.hd, HasName.hd with | .((nth ((snm, sτ) :: sch) { val := 0, isLt := hlt }.val (_ : { val := 0, isLt := hlt }.val < length ((snm, sτ) :: sch))).fst), Sum.inl (EqT.refl .((nth ((snm, sτ) :: sch) { val := 0, isLt := hlt }.val (_ : { val := 0, isLt := hlt }.val < length ((snm, sτ) :: sch))).fst)), h => hasNthName { val := 0, isLt := hlt } | hdr, Sum.inr hhnm, h => hasNameOfNthsHasName hhnm }
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.lookupType_nths_eq_lookupType
[372, 1]
[413, 28]
simp only [Schema.hasNameEqHeadOrTail, Schema.hasNthName, Schema.lookupType]
η : Type u_η dec_η : DecidableEq η schema : Schema snm : η sτ : Type u_1 sch : List Header hlt : 0 < length ((snm, sτ) :: sch) ns : List (Fin (length ((snm, sτ) :: sch))) ⊢ sτ = lookupType ((snm, sτ) :: sch) { fst := snm, snd := match snm, hasNameEqHeadOrTail HasName.hd, HasName.hd with | .((nth ((snm, sτ) :: sch) { val := 0, isLt := hlt }.val (_ : { val := 0, isLt := hlt }.val < length ((snm, sτ) :: sch))).fst), Sum.inl (EqT.refl .((nth ((snm, sτ) :: sch) { val := 0, isLt := hlt }.val (_ : { val := 0, isLt := hlt }.val < length ((snm, sτ) :: sch))).fst)), h => hasNthName { val := 0, isLt := hlt } | hdr, Sum.inr hhnm, h => hasNameOfNthsHasName hhnm }
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.lookupType_nths_eq_lookupType
[372, 1]
[413, 28]
conv => lhs simp only [Schema.nths, Schema.map, Schema.lookupType]
η : Type u_η dec_η : DecidableEq η schema : Schema snm : η sτ : Type u_1 sch : List Header hlt : 0 < length ((snm, sτ) :: sch) ns : List (Fin (length ((snm, sτ) :: sch))) nm : η h : HasName nm (map (fun n => nth ((snm, sτ) :: sch) n.val (_ : n.val < length ((snm, sτ) :: sch))) ns) ⊢ lookupType (nths ((snm, sτ) :: sch) ({ val := 0, isLt := hlt } :: ns)) { fst := nm, snd := HasName.tl h } = lookupType ((snm, sτ) :: sch) { fst := nm, snd := hasNameOfNthsHasName (HasName.tl h) }
η : Type u_η dec_η : DecidableEq η schema : Schema snm : η sτ : Type u_1 sch : List Header hlt : 0 < length ((snm, sτ) :: sch) ns : List (Fin (length ((snm, sτ) :: sch))) nm : η h : HasName nm (map (fun n => nth ((snm, sτ) :: sch) n.val (_ : n.val < length ((snm, sτ) :: sch))) ns) ⊢ lookupType (map (fun n => nth ((snm, sτ) :: sch) n.val (_ : n.val < length ((snm, sτ) :: sch))) ns) { fst := nm, snd := h } = lookupType ((snm, sτ) :: sch) { fst := nm, snd := hasNameOfNthsHasName (HasName.tl h) }
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.lookupType_nths_eq_lookupType
[372, 1]
[413, 28]
conv => rhs unfold Schema.hasNameOfNthsHasName simp only [Schema.hasNameEqHeadOrTail]
η : Type u_η dec_η : DecidableEq η schema : Schema snm : η sτ : Type u_1 sch : List Header hlt : 0 < length ((snm, sτ) :: sch) ns : List (Fin (length ((snm, sτ) :: sch))) nm : η h : HasName nm (map (fun n => nth ((snm, sτ) :: sch) n.val (_ : n.val < length ((snm, sτ) :: sch))) ns) ⊢ lookupType (map (fun n => nth ((snm, sτ) :: sch) n.val (_ : n.val < length ((snm, sτ) :: sch))) ns) { fst := nm, snd := h } = lookupType ((snm, sτ) :: sch) { fst := nm, snd := hasNameOfNthsHasName (HasName.tl h) }
η : Type u_η dec_η : DecidableEq η schema : Schema snm : η sτ : Type u_1 sch : List Header hlt : 0 < length ((snm, sτ) :: sch) ns : List (Fin (length ((snm, sτ) :: sch))) nm : η h : HasName nm (map (fun n => nth ((snm, sτ) :: sch) n.val (_ : n.val < length ((snm, sτ) :: sch))) ns) ⊢ lookupType (map (fun n => nth ((snm, sτ) :: sch) n.val (_ : n.val < length ((snm, sτ) :: sch))) ns) { fst := nm, snd := h } = lookupType ((snm, sτ) :: sch) { fst := nm, snd := hasNameOfNthsHasName h }
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.lookupType_nths_eq_lookupType
[372, 1]
[413, 28]
apply lookupType_nths_eq_lookupType
η : Type u_η dec_η : DecidableEq η schema : Schema snm : η sτ : Type u_1 sch : List Header hlt : 0 < length ((snm, sτ) :: sch) ns : List (Fin (length ((snm, sτ) :: sch))) nm : η h : HasName nm (map (fun n => nth ((snm, sτ) :: sch) n.val (_ : n.val < length ((snm, sτ) :: sch))) ns) ⊢ lookupType (map (fun n => nth ((snm, sτ) :: sch) n.val (_ : n.val < length ((snm, sτ) :: sch))) ns) { fst := nm, snd := h } = lookupType ((snm, sτ) :: sch) { fst := nm, snd := hasNameOfNthsHasName h }
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.lookupType_nths_eq_lookupType
[372, 1]
[413, 28]
conv => rhs unfold Schema.hasNameOfNthsHasName simp only [h]
η : Type u_η dec_η : DecidableEq η schema : Schema snm : η sτ : Type u_1 sch : List Header n : Nat pf : Nat.succ n < length ((snm, sτ) :: sch) ns : List (Fin (length ((snm, sτ) :: sch))) nm : η hnths : HasName nm (nths ((snm, sτ) :: sch) ({ val := Nat.succ n, isLt := pf } :: ns)) hhnm : HasName nm (map (fun n => nth ((snm, sτ) :: sch) n.val (_ : n.val < length ((snm, sτ) :: sch))) ns) h : hasNameEqHeadOrTail hnths = Sum.inr hhnm ⊢ lookupType (nths ((snm, sτ) :: sch) ({ val := Nat.succ n, isLt := pf } :: ns)) { fst := nm, snd := hnths } = lookupType ((snm, sτ) :: sch) { fst := nm, snd := hasNameOfNthsHasName hnths }
η : Type u_η dec_η : DecidableEq η schema : Schema snm : η sτ : Type u_1 sch : List Header n : Nat pf : Nat.succ n < length ((snm, sτ) :: sch) ns : List (Fin (length ((snm, sτ) :: sch))) nm : η hnths : HasName nm (nths ((snm, sτ) :: sch) ({ val := Nat.succ n, isLt := pf } :: ns)) hhnm : HasName nm (map (fun n => nth ((snm, sτ) :: sch) n.val (_ : n.val < length ((snm, sτ) :: sch))) ns) h : hasNameEqHeadOrTail hnths = Sum.inr hhnm ⊢ lookupType (nths ((snm, sτ) :: sch) ({ val := Nat.succ n, isLt := pf } :: ns)) { fst := nm, snd := hnths } = lookupType ((snm, sτ) :: sch) { fst := nm, snd := hasNameOfNthsHasName hhnm }
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/SchemaFunctions.lean
Schema.lookupType_nths_eq_lookupType
[372, 1]
[413, 28]
have htoprove : hnths = .tl hhnm := Schema.hasNameEqHeadOrTail_inr _ _ (EqT.ofEq h)
η : Type u_η dec_η : DecidableEq η schema : Schema snm : η sτ : Type u_1 sch : List Header n : Nat pf : Nat.succ n < length ((snm, sτ) :: sch) ns : List (Fin (length ((snm, sτ) :: sch))) nm : η hnths : HasName nm (nths ((snm, sτ) :: sch) ({ val := Nat.succ n, isLt := pf } :: ns)) hhnm : HasName nm (map (fun n => nth ((snm, sτ) :: sch) n.val (_ : n.val < length ((snm, sτ) :: sch))) ns) h : hasNameEqHeadOrTail hnths = Sum.inr hhnm ⊢ lookupType (nths ((snm, sτ) :: sch) ({ val := Nat.succ n, isLt := pf } :: ns)) { fst := nm, snd := hnths } = lookupType ((snm, sτ) :: sch) { fst := nm, snd := hasNameOfNthsHasName hhnm }
η : Type u_η dec_η : DecidableEq η schema : Schema snm : η sτ : Type u_1 sch : List Header n : Nat pf : Nat.succ n < length ((snm, sτ) :: sch) ns : List (Fin (length ((snm, sτ) :: sch))) nm : η hnths : HasName nm (nths ((snm, sτ) :: sch) ({ val := Nat.succ n, isLt := pf } :: ns)) hhnm : HasName nm (map (fun n => nth ((snm, sτ) :: sch) n.val (_ : n.val < length ((snm, sτ) :: sch))) ns) h : hasNameEqHeadOrTail hnths = Sum.inr hhnm htoprove : hnths = HasName.tl hhnm ⊢ lookupType (nths ((snm, sτ) :: sch) ({ val := Nat.succ n, isLt := pf } :: ns)) { fst := nm, snd := hnths } = lookupType ((snm, sτ) :: sch) { fst := nm, snd := hasNameOfNthsHasName hhnm }