url
stringclasses 147
values | commit
stringclasses 147
values | file_path
stringlengths 7
101
| full_name
stringlengths 1
94
| start
stringlengths 6
10
| end
stringlengths 6
11
| tactic
stringlengths 1
11.2k
| state_before
stringlengths 3
2.09M
| state_after
stringlengths 6
2.09M
|
|---|---|---|---|---|---|---|---|---|
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Schema.lean | Schema.lookupType_eq_snd_lookup | [371, 1] | [381, 13] | cases cn with | mk nm pf =>
induction pf with
| hd =>
simp only [lookupType]
rw [lookup_eq_1]
| tl h ih =>
simp only [lookupType]
rw [lookup_eq_2]
apply ih | η : Type u_η
dec_η : DecidableEq η
schema : Schema
s : Schema
cn : CertifiedName s
⊢ lookupType s cn = (lookup s cn).snd | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Schema.lean | Schema.lookupType_eq_snd_lookup | [371, 1] | [381, 13] | induction pf with
| hd =>
simp only [lookupType]
rw [lookup_eq_1]
| tl h ih =>
simp only [lookupType]
rw [lookup_eq_2]
apply ih | case mk
η : Type u_η
dec_η : DecidableEq η
schema : Schema
s : Schema
nm : η
pf : HasName nm s
⊢ lookupType s { fst := nm, snd := pf } = (lookup s { fst := nm, snd := pf }).snd | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Schema.lean | Schema.lookupType_eq_snd_lookup | [371, 1] | [381, 13] | simp only [lookupType] | case mk.hd
η : Type u_η
dec_η : DecidableEq η
schema : Schema
s : Schema
nm c✝ : η
rs✝ : Schema
τ✝ : Type u_1
⊢ lookupType ((c✝, τ✝) :: rs✝) { fst := c✝, snd := HasName.hd } =
(lookup ((c✝, τ✝) :: rs✝) { fst := c✝, snd := HasName.hd }).snd | case mk.hd
η : Type u_η
dec_η : DecidableEq η
schema : Schema
s : Schema
nm c✝ : η
rs✝ : Schema
τ✝ : Type u_1
⊢ τ✝ = (lookup ((c✝, τ✝) :: rs✝) { fst := c✝, snd := HasName.hd }).snd |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Schema.lean | Schema.lookupType_eq_snd_lookup | [371, 1] | [381, 13] | rw [lookup_eq_1] | case mk.hd
η : Type u_η
dec_η : DecidableEq η
schema : Schema
s : Schema
nm c✝ : η
rs✝ : Schema
τ✝ : Type u_1
⊢ τ✝ = (lookup ((c✝, τ✝) :: rs✝) { fst := c✝, snd := HasName.hd }).snd | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Schema.lean | Schema.lookupType_eq_snd_lookup | [371, 1] | [381, 13] | simp only [lookupType] | case mk.tl
η : Type u_η
dec_η : DecidableEq η
schema : Schema
s : Schema
nm : η
r✝ : Header
c✝ : η
rs✝ : Schema
h : HasName c✝ rs✝
ih : lookupType rs✝ { fst := c✝, snd := h } = (lookup rs✝ { fst := c✝, snd := h }).snd
⊢ lookupType (r✝ :: rs✝) { fst := c✝, snd := HasName.tl h } =
(lookup (r✝ :: rs✝) { fst := c✝, snd := HasName.tl h }).snd | case mk.tl
η : Type u_η
dec_η : DecidableEq η
schema : Schema
s : Schema
nm : η
r✝ : Header
c✝ : η
rs✝ : Schema
h : HasName c✝ rs✝
ih : lookupType rs✝ { fst := c✝, snd := h } = (lookup rs✝ { fst := c✝, snd := h }).snd
⊢ lookupType rs✝ { fst := c✝, snd := h } = (lookup (r✝ :: rs✝) { fst := c✝, snd := HasName.tl h }).snd |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Schema.lean | Schema.lookupType_eq_snd_lookup | [371, 1] | [381, 13] | rw [lookup_eq_2] | case mk.tl
η : Type u_η
dec_η : DecidableEq η
schema : Schema
s : Schema
nm : η
r✝ : Header
c✝ : η
rs✝ : Schema
h : HasName c✝ rs✝
ih : lookupType rs✝ { fst := c✝, snd := h } = (lookup rs✝ { fst := c✝, snd := h }).snd
⊢ lookupType rs✝ { fst := c✝, snd := h } = (lookup (r✝ :: rs✝) { fst := c✝, snd := HasName.tl h }).snd | case mk.tl
η : Type u_η
dec_η : DecidableEq η
schema : Schema
s : Schema
nm : η
r✝ : Header
c✝ : η
rs✝ : Schema
h : HasName c✝ rs✝
ih : lookupType rs✝ { fst := c✝, snd := h } = (lookup rs✝ { fst := c✝, snd := h }).snd
⊢ lookupType rs✝ { fst := c✝, snd := h } = (lookup rs✝ { fst := c✝, snd := h }).snd |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Schema.lean | Schema.lookupType_eq_snd_lookup | [371, 1] | [381, 13] | apply ih | case mk.tl
η : Type u_η
dec_η : DecidableEq η
schema : Schema
s : Schema
nm : η
r✝ : Header
c✝ : η
rs✝ : Schema
h : HasName c✝ rs✝
ih : lookupType rs✝ { fst := c✝, snd := h } = (lookup rs✝ { fst := c✝, snd := h }).snd
⊢ lookupType rs✝ { fst := c✝, snd := h } = (lookup rs✝ { fst := c✝, snd := h }).snd | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | addRows_spec2 | [20, 1] | [25, 37] | intro t rs | η : Type u_η
dec_η : DecidableEq η
sch : Schema
⊢ ∀ (t : Table sch) (rs : List (Row sch)), nrows (addRows t rs) = nrows t + List.length rs | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
rs : List (Row sch)
⊢ nrows (addRows t rs) = nrows t + List.length rs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | addRows_spec2 | [20, 1] | [25, 37] | simp only [nrows, Schema.length_eq_List_length] | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
rs : List (Row sch)
⊢ nrows (addRows t rs) = nrows t + List.length rs | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
rs : List (Row sch)
⊢ List.length (addRows t rs).rows = List.length t.rows + List.length rs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | addRows_spec2 | [20, 1] | [25, 37] | exact List.length_append t.rows rs | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
rs : List (Row sch)
⊢ List.length (addRows t rs).rows = List.length t.rows + List.length rs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | addColumn_spec1 | [32, 1] | [47, 25] | intros τ inst t c vs | η : Type u_η
dec_η : DecidableEq η
sch : Schema
⊢ ∀ {τ : Type u} [inst : DecidableEq τ] (t : Table sch) (c : η) (vs : List (Option τ)),
header (addColumn t c vs) = List.append (header t) [c] | η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst : DecidableEq τ
t : Table sch
c : η
vs : List (Option τ)
⊢ header (addColumn t c vs) = List.append (header t) [c] |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | addColumn_spec1 | [32, 1] | [47, 25] | simp [header, addColumn, Schema.names] | η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst : DecidableEq τ
t : Table sch
c : η
vs : List (Option τ)
⊢ header (addColumn t c vs) = List.append (header t) [c] | η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst : DecidableEq τ
t : Table sch
c : η
vs : List (Option τ)
⊢ List.map Prod.fst (Schema.append sch [(c, τ)]) = List.map Prod.fst sch ++ [c] |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | addColumn_spec1 | [32, 1] | [47, 25] | induction sch with
| nil => simp [List.map, List.append]
| cons s ss ih =>
simp only [List.map]
rw [ih]
simp [List.append]
exact dropColumn t _ | η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst : DecidableEq τ
t : Table sch
c : η
vs : List (Option τ)
⊢ List.map Prod.fst (Schema.append sch [(c, τ)]) = List.map Prod.fst sch ++ [c] | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | addColumn_spec1 | [32, 1] | [47, 25] | simp [List.map, List.append] | case nil
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst : DecidableEq τ
c : η
vs : List (Option τ)
t : Table []
⊢ List.map Prod.fst (Schema.append [] [(c, τ)]) = List.map Prod.fst [] ++ [c] | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | addColumn_spec1 | [32, 1] | [47, 25] | simp only [List.map] | case cons
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst : DecidableEq τ
c : η
vs : List (Option τ)
s : Header
ss : List Header
ih : Table ss → List.map Prod.fst (Schema.append ss [(c, τ)]) = List.map Prod.fst ss ++ [c]
t : Table (s :: ss)
⊢ List.map Prod.fst (Schema.append (s :: ss) [(c, τ)]) = List.map Prod.fst (s :: ss) ++ [c] | case cons
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst : DecidableEq τ
c : η
vs : List (Option τ)
s : Header
ss : List Header
ih : Table ss → List.map Prod.fst (Schema.append ss [(c, τ)]) = List.map Prod.fst ss ++ [c]
t : Table (s :: ss)
⊢ s.fst :: List.map Prod.fst (Schema.append ss [(c, τ)]) = s.fst :: List.map Prod.fst ss ++ [c] |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | addColumn_spec1 | [32, 1] | [47, 25] | rw [ih] | case cons
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst : DecidableEq τ
c : η
vs : List (Option τ)
s : Header
ss : List Header
ih : Table ss → List.map Prod.fst (Schema.append ss [(c, τ)]) = List.map Prod.fst ss ++ [c]
t : Table (s :: ss)
⊢ s.fst :: List.map Prod.fst (Schema.append ss [(c, τ)]) = s.fst :: List.map Prod.fst ss ++ [c] | case cons
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst : DecidableEq τ
c : η
vs : List (Option τ)
s : Header
ss : List Header
ih : Table ss → List.map Prod.fst (Schema.append ss [(c, τ)]) = List.map Prod.fst ss ++ [c]
t : Table (s :: ss)
⊢ s.fst :: (List.map Prod.fst ss ++ [c]) = s.fst :: List.map Prod.fst ss ++ [c]
case cons
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst : DecidableEq τ
c : η
vs : List (Option τ)
s : Header
ss : List Header
ih : Table ss → List.map Prod.fst (Schema.append ss [(c, τ)]) = List.map Prod.fst ss ++ [c]
t : Table (s :: ss)
⊢ Table ss |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | addColumn_spec1 | [32, 1] | [47, 25] | simp [List.append] | case cons
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst : DecidableEq τ
c : η
vs : List (Option τ)
s : Header
ss : List Header
ih : Table ss → List.map Prod.fst (Schema.append ss [(c, τ)]) = List.map Prod.fst ss ++ [c]
t : Table (s :: ss)
⊢ s.fst :: (List.map Prod.fst ss ++ [c]) = s.fst :: List.map Prod.fst ss ++ [c]
case cons
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst : DecidableEq τ
c : η
vs : List (Option τ)
s : Header
ss : List Header
ih : Table ss → List.map Prod.fst (Schema.append ss [(c, τ)]) = List.map Prod.fst ss ++ [c]
t : Table (s :: ss)
⊢ Table ss | case cons
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst : DecidableEq τ
c : η
vs : List (Option τ)
s : Header
ss : List Header
ih : Table ss → List.map Prod.fst (Schema.append ss [(c, τ)]) = List.map Prod.fst ss ++ [c]
t : Table (s :: ss)
⊢ Table ss |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | addColumn_spec1 | [32, 1] | [47, 25] | exact dropColumn t _ | case cons
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst : DecidableEq τ
c : η
vs : List (Option τ)
s : Header
ss : List Header
ih : Table ss → List.map Prod.fst (Schema.append ss [(c, τ)]) = List.map Prod.fst ss ++ [c]
t : Table (s :: ss)
⊢ Table ss | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | addColumn_spec3 | [63, 1] | [75, 30] | intros t c vs | η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst✝ : DecidableEq τ
⊢ ∀ (t : Table sch) (c : η) (vs : List (Option τ)),
Schema.lookupType (schema (addColumn t c vs))
{ fst := c, snd := Schema.colImpliesName (Schema.hasAppendedHead sch c τ []) } =
τ | η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst✝ : DecidableEq τ
t : Table sch
c : η
vs : List (Option τ)
⊢ Schema.lookupType (schema (addColumn t c vs))
{ fst := c, snd := Schema.colImpliesName (Schema.hasAppendedHead sch c τ []) } =
τ |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | addColumn_spec3 | [63, 1] | [75, 30] | induction sch with
| nil =>
simp only [Schema.lookupType]
| cons s ss ih =>
simp only [Schema.lookupType]
apply ih (dropColumn t _) | η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst✝ : DecidableEq τ
t : Table sch
c : η
vs : List (Option τ)
⊢ Schema.lookupType (schema (addColumn t c vs))
{ fst := c, snd := Schema.colImpliesName (Schema.hasAppendedHead sch c τ []) } =
τ | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | addColumn_spec3 | [63, 1] | [75, 30] | simp only [Schema.lookupType] | case nil
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst✝ : DecidableEq τ
c : η
vs : List (Option τ)
t : Table []
⊢ Schema.lookupType (schema (addColumn t c vs))
{ fst := c, snd := Schema.colImpliesName (Schema.hasAppendedHead [] c τ []) } =
τ | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | addColumn_spec3 | [63, 1] | [75, 30] | simp only [Schema.lookupType] | case cons
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst✝ : DecidableEq τ
c : η
vs : List (Option τ)
s : Header
ss : List Header
ih :
∀ (t : Table ss),
Schema.lookupType (schema (addColumn t c vs))
{ fst := c, snd := Schema.colImpliesName (Schema.hasAppendedHead ss c τ []) } =
τ
t : Table (s :: ss)
⊢ Schema.lookupType (schema (addColumn t c vs))
{ fst := c, snd := Schema.colImpliesName (Schema.hasAppendedHead (s :: ss) c τ []) } =
τ | case cons
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst✝ : DecidableEq τ
c : η
vs : List (Option τ)
s : Header
ss : List Header
ih :
∀ (t : Table ss),
Schema.lookupType (schema (addColumn t c vs))
{ fst := c, snd := Schema.colImpliesName (Schema.hasAppendedHead ss c τ []) } =
τ
t : Table (s :: ss)
⊢ Schema.lookupType (Schema.append ss [(c, τ)])
{ fst := c, snd := Schema.colImpliesName (Schema.hasAppendedHead ss c τ []) } =
τ |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | addColumn_spec3 | [63, 1] | [75, 30] | apply ih (dropColumn t _) | case cons
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst✝ : DecidableEq τ
c : η
vs : List (Option τ)
s : Header
ss : List Header
ih :
∀ (t : Table ss),
Schema.lookupType (schema (addColumn t c vs))
{ fst := c, snd := Schema.colImpliesName (Schema.hasAppendedHead ss c τ []) } =
τ
t : Table (s :: ss)
⊢ Schema.lookupType (Schema.append ss [(c, τ)])
{ fst := c, snd := Schema.colImpliesName (Schema.hasAppendedHead ss c τ []) } =
τ | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | addColumn_spec4 | [77, 1] | [85, 18] | intros τ inst t c vs h | η : Type u_η
dec_η : DecidableEq η
sch : Schema
⊢ ∀ {τ : Type u} [inst : DecidableEq τ] (t : Table sch) (c : η) (vs : List (Option τ)),
List.length vs = nrows t → nrows (addColumn t c vs) = nrows t | η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst : DecidableEq τ
t : Table sch
c : η
vs : List (Option τ)
h : List.length vs = nrows t
⊢ nrows (addColumn t c vs) = nrows t |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | addColumn_spec4 | [77, 1] | [85, 18] | simp only [nrows, addColumn, Schema.length_eq_List_length] at * | η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst : DecidableEq τ
t : Table sch
c : η
vs : List (Option τ)
h : List.length vs = nrows t
⊢ nrows (addColumn t c vs) = nrows t | η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst : DecidableEq τ
t : Table sch
c : η
vs : List (Option τ)
h : List.length vs = List.length t.rows
⊢ List.length (List.map (fun x => Row.addColumn x.fst c x.snd) (List.zip t.rows vs)) = List.length t.rows |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | addColumn_spec4 | [77, 1] | [85, 18] | simp only [List.length_map] | η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst : DecidableEq τ
t : Table sch
c : η
vs : List (Option τ)
h : List.length vs = List.length t.rows
⊢ List.length (List.map (fun x => Row.addColumn x.fst c x.snd) (List.zip t.rows vs)) = List.length t.rows | η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst : DecidableEq τ
t : Table sch
c : η
vs : List (Option τ)
h : List.length vs = List.length t.rows
⊢ List.length (List.zip t.rows vs) = List.length t.rows |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | addColumn_spec4 | [77, 1] | [85, 18] | rw [List.zip_length_eq_of_length_eq] | η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst : DecidableEq τ
t : Table sch
c : η
vs : List (Option τ)
h : List.length vs = List.length t.rows
⊢ List.length (List.zip t.rows vs) = List.length t.rows | case h
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst : DecidableEq τ
t : Table sch
c : η
vs : List (Option τ)
h : List.length vs = List.length t.rows
⊢ List.length t.rows = List.length vs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | addColumn_spec4 | [77, 1] | [85, 18] | exact Eq.symm h | case h
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst : DecidableEq τ
t : Table sch
c : η
vs : List (Option τ)
h : List.length vs = List.length t.rows
⊢ List.length t.rows = List.length vs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | buildColumn_spec2 | [90, 1] | [102, 43] | intros τ t c f | η : Type u_η
dec_η : DecidableEq η
sch : Schema
⊢ ∀ {τ : Type u} (t : Table sch) (c : η) (f : Row sch → Option τ),
header (buildColumn t c f) = List.append (header t) [c] | η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
t : Table sch
c : η
f : Row sch → Option τ
⊢ header (buildColumn t c f) = List.append (header t) [c] |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | buildColumn_spec2 | [90, 1] | [102, 43] | simp [header, Schema.names] | η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
t : Table sch
c : η
f : Row sch → Option τ
⊢ header (buildColumn t c f) = List.append (header t) [c] | η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
t : Table sch
c : η
f : Row sch → Option τ
⊢ List.map Prod.fst (Schema.append sch [(c, τ)]) = List.map Prod.fst sch ++ [c] |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | buildColumn_spec2 | [90, 1] | [102, 43] | induction sch with
| nil => simp [List.map, List.append]
| cons s ss ih =>
simp only [List.map]
rw [ih]
simp [List.append]
exact Table.mk []
exact (λ x => f (Row.cons Cell.emp x)) | η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
t : Table sch
c : η
f : Row sch → Option τ
⊢ List.map Prod.fst (Schema.append sch [(c, τ)]) = List.map Prod.fst sch ++ [c] | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | buildColumn_spec2 | [90, 1] | [102, 43] | simp [List.map, List.append] | case nil
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
c : η
t : Table []
f : Row [] → Option τ
⊢ List.map Prod.fst (Schema.append [] [(c, τ)]) = List.map Prod.fst [] ++ [c] | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | buildColumn_spec2 | [90, 1] | [102, 43] | simp only [List.map] | case cons
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
c : η
s : Header
ss : List Header
ih : Table ss → (Row ss → Option τ) → List.map Prod.fst (Schema.append ss [(c, τ)]) = List.map Prod.fst ss ++ [c]
t : Table (s :: ss)
f : Row (s :: ss) → Option τ
⊢ List.map Prod.fst (Schema.append (s :: ss) [(c, τ)]) = List.map Prod.fst (s :: ss) ++ [c] | case cons
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
c : η
s : Header
ss : List Header
ih : Table ss → (Row ss → Option τ) → List.map Prod.fst (Schema.append ss [(c, τ)]) = List.map Prod.fst ss ++ [c]
t : Table (s :: ss)
f : Row (s :: ss) → Option τ
⊢ s.fst :: List.map Prod.fst (Schema.append ss [(c, τ)]) = s.fst :: List.map Prod.fst ss ++ [c] |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | buildColumn_spec2 | [90, 1] | [102, 43] | rw [ih] | case cons
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
c : η
s : Header
ss : List Header
ih : Table ss → (Row ss → Option τ) → List.map Prod.fst (Schema.append ss [(c, τ)]) = List.map Prod.fst ss ++ [c]
t : Table (s :: ss)
f : Row (s :: ss) → Option τ
⊢ s.fst :: List.map Prod.fst (Schema.append ss [(c, τ)]) = s.fst :: List.map Prod.fst ss ++ [c] | case cons
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
c : η
s : Header
ss : List Header
ih : Table ss → (Row ss → Option τ) → List.map Prod.fst (Schema.append ss [(c, τ)]) = List.map Prod.fst ss ++ [c]
t : Table (s :: ss)
f : Row (s :: ss) → Option τ
⊢ s.fst :: (List.map Prod.fst ss ++ [c]) = s.fst :: List.map Prod.fst ss ++ [c]
case cons.t
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
c : η
s : Header
ss : List Header
ih : Table ss → (Row ss → Option τ) → List.map Prod.fst (Schema.append ss [(c, τ)]) = List.map Prod.fst ss ++ [c]
t : Table (s :: ss)
f : Row (s :: ss) → Option τ
⊢ Table ss
case cons.f
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
c : η
s : Header
ss : List Header
ih : Table ss → (Row ss → Option τ) → List.map Prod.fst (Schema.append ss [(c, τ)]) = List.map Prod.fst ss ++ [c]
t : Table (s :: ss)
f : Row (s :: ss) → Option τ
⊢ Row ss → Option τ |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | buildColumn_spec2 | [90, 1] | [102, 43] | simp [List.append] | case cons
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
c : η
s : Header
ss : List Header
ih : Table ss → (Row ss → Option τ) → List.map Prod.fst (Schema.append ss [(c, τ)]) = List.map Prod.fst ss ++ [c]
t : Table (s :: ss)
f : Row (s :: ss) → Option τ
⊢ s.fst :: (List.map Prod.fst ss ++ [c]) = s.fst :: List.map Prod.fst ss ++ [c]
case cons.t
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
c : η
s : Header
ss : List Header
ih : Table ss → (Row ss → Option τ) → List.map Prod.fst (Schema.append ss [(c, τ)]) = List.map Prod.fst ss ++ [c]
t : Table (s :: ss)
f : Row (s :: ss) → Option τ
⊢ Table ss
case cons.f
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
c : η
s : Header
ss : List Header
ih : Table ss → (Row ss → Option τ) → List.map Prod.fst (Schema.append ss [(c, τ)]) = List.map Prod.fst ss ++ [c]
t : Table (s :: ss)
f : Row (s :: ss) → Option τ
⊢ Row ss → Option τ | case cons.t
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
c : η
s : Header
ss : List Header
ih : Table ss → (Row ss → Option τ) → List.map Prod.fst (Schema.append ss [(c, τ)]) = List.map Prod.fst ss ++ [c]
t : Table (s :: ss)
f : Row (s :: ss) → Option τ
⊢ Table ss
case cons.f
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
c : η
s : Header
ss : List Header
ih : Table ss → (Row ss → Option τ) → List.map Prod.fst (Schema.append ss [(c, τ)]) = List.map Prod.fst ss ++ [c]
t : Table (s :: ss)
f : Row (s :: ss) → Option τ
⊢ Row ss → Option τ |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | buildColumn_spec2 | [90, 1] | [102, 43] | exact Table.mk [] | case cons.t
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
c : η
s : Header
ss : List Header
ih : Table ss → (Row ss → Option τ) → List.map Prod.fst (Schema.append ss [(c, τ)]) = List.map Prod.fst ss ++ [c]
t : Table (s :: ss)
f : Row (s :: ss) → Option τ
⊢ Table ss
case cons.f
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
c : η
s : Header
ss : List Header
ih : Table ss → (Row ss → Option τ) → List.map Prod.fst (Schema.append ss [(c, τ)]) = List.map Prod.fst ss ++ [c]
t : Table (s :: ss)
f : Row (s :: ss) → Option τ
⊢ Row ss → Option τ | case cons.f
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
c : η
s : Header
ss : List Header
ih : Table ss → (Row ss → Option τ) → List.map Prod.fst (Schema.append ss [(c, τ)]) = List.map Prod.fst ss ++ [c]
t : Table (s :: ss)
f : Row (s :: ss) → Option τ
⊢ Row ss → Option τ |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | buildColumn_spec2 | [90, 1] | [102, 43] | exact (λ x => f (Row.cons Cell.emp x)) | case cons.f
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
c : η
s : Header
ss : List Header
ih : Table ss → (Row ss → Option τ) → List.map Prod.fst (Schema.append ss [(c, τ)]) = List.map Prod.fst ss ++ [c]
t : Table (s :: ss)
f : Row (s :: ss) → Option τ
⊢ Row ss → Option τ | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | buildColumn_spec4 | [115, 1] | [127, 36] | intros t c f | η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst✝ : DecidableEq τ
⊢ ∀ (t : Table sch) (c : η) (f : Row sch → Option τ),
Schema.lookupType (schema (buildColumn t c f))
{ fst := c, snd := Schema.colImpliesName (Schema.hasAppendedHead sch c τ []) } =
τ | η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst✝ : DecidableEq τ
t : Table sch
c : η
f : Row sch → Option τ
⊢ Schema.lookupType (schema (buildColumn t c f))
{ fst := c, snd := Schema.colImpliesName (Schema.hasAppendedHead sch c τ []) } =
τ |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | buildColumn_spec4 | [115, 1] | [127, 36] | induction sch with
| nil =>
simp only [Schema.lookupType]
| cons s ss ih =>
simp only [Schema.lookupType]
apply ih
. exact (dropColumn t _)
. exact f ∘ (Row.cons Cell.emp) | η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst✝ : DecidableEq τ
t : Table sch
c : η
f : Row sch → Option τ
⊢ Schema.lookupType (schema (buildColumn t c f))
{ fst := c, snd := Schema.colImpliesName (Schema.hasAppendedHead sch c τ []) } =
τ | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | buildColumn_spec4 | [115, 1] | [127, 36] | simp only [Schema.lookupType] | case nil
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst✝ : DecidableEq τ
c : η
t : Table []
f : Row [] → Option τ
⊢ Schema.lookupType (schema (buildColumn t c f))
{ fst := c, snd := Schema.colImpliesName (Schema.hasAppendedHead [] c τ []) } =
τ | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | buildColumn_spec4 | [115, 1] | [127, 36] | simp only [Schema.lookupType] | case cons
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst✝ : DecidableEq τ
c : η
s : Header
ss : List Header
ih :
∀ (t : Table ss) (f : Row ss → Option τ),
Schema.lookupType (schema (buildColumn t c f))
{ fst := c, snd := Schema.colImpliesName (Schema.hasAppendedHead ss c τ []) } =
τ
t : Table (s :: ss)
f : Row (s :: ss) → Option τ
⊢ Schema.lookupType (schema (buildColumn t c f))
{ fst := c, snd := Schema.colImpliesName (Schema.hasAppendedHead (s :: ss) c τ []) } =
τ | case cons
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst✝ : DecidableEq τ
c : η
s : Header
ss : List Header
ih :
∀ (t : Table ss) (f : Row ss → Option τ),
Schema.lookupType (schema (buildColumn t c f))
{ fst := c, snd := Schema.colImpliesName (Schema.hasAppendedHead ss c τ []) } =
τ
t : Table (s :: ss)
f : Row (s :: ss) → Option τ
⊢ Schema.lookupType (Schema.append ss [(c, τ)])
{ fst := c, snd := Schema.colImpliesName (Schema.hasAppendedHead ss c τ []) } =
τ |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | buildColumn_spec4 | [115, 1] | [127, 36] | apply ih | case cons
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst✝ : DecidableEq τ
c : η
s : Header
ss : List Header
ih :
∀ (t : Table ss) (f : Row ss → Option τ),
Schema.lookupType (schema (buildColumn t c f))
{ fst := c, snd := Schema.colImpliesName (Schema.hasAppendedHead ss c τ []) } =
τ
t : Table (s :: ss)
f : Row (s :: ss) → Option τ
⊢ Schema.lookupType (Schema.append ss [(c, τ)])
{ fst := c, snd := Schema.colImpliesName (Schema.hasAppendedHead ss c τ []) } =
τ | case cons.t
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst✝ : DecidableEq τ
c : η
s : Header
ss : List Header
ih :
∀ (t : Table ss) (f : Row ss → Option τ),
Schema.lookupType (schema (buildColumn t c f))
{ fst := c, snd := Schema.colImpliesName (Schema.hasAppendedHead ss c τ []) } =
τ
t : Table (s :: ss)
f : Row (s :: ss) → Option τ
⊢ Table ss
case cons.f
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst✝ : DecidableEq τ
c : η
s : Header
ss : List Header
ih :
∀ (t : Table ss) (f : Row ss → Option τ),
Schema.lookupType (schema (buildColumn t c f))
{ fst := c, snd := Schema.colImpliesName (Schema.hasAppendedHead ss c τ []) } =
τ
t : Table (s :: ss)
f : Row (s :: ss) → Option τ
⊢ Row ss → Option τ |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | buildColumn_spec4 | [115, 1] | [127, 36] | . exact (dropColumn t _) | case cons.t
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst✝ : DecidableEq τ
c : η
s : Header
ss : List Header
ih :
∀ (t : Table ss) (f : Row ss → Option τ),
Schema.lookupType (schema (buildColumn t c f))
{ fst := c, snd := Schema.colImpliesName (Schema.hasAppendedHead ss c τ []) } =
τ
t : Table (s :: ss)
f : Row (s :: ss) → Option τ
⊢ Table ss
case cons.f
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst✝ : DecidableEq τ
c : η
s : Header
ss : List Header
ih :
∀ (t : Table ss) (f : Row ss → Option τ),
Schema.lookupType (schema (buildColumn t c f))
{ fst := c, snd := Schema.colImpliesName (Schema.hasAppendedHead ss c τ []) } =
τ
t : Table (s :: ss)
f : Row (s :: ss) → Option τ
⊢ Row ss → Option τ | case cons.f
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst✝ : DecidableEq τ
c : η
s : Header
ss : List Header
ih :
∀ (t : Table ss) (f : Row ss → Option τ),
Schema.lookupType (schema (buildColumn t c f))
{ fst := c, snd := Schema.colImpliesName (Schema.hasAppendedHead ss c τ []) } =
τ
t : Table (s :: ss)
f : Row (s :: ss) → Option τ
⊢ Row ss → Option τ |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | buildColumn_spec4 | [115, 1] | [127, 36] | . exact f ∘ (Row.cons Cell.emp) | case cons.f
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst✝ : DecidableEq τ
c : η
s : Header
ss : List Header
ih :
∀ (t : Table ss) (f : Row ss → Option τ),
Schema.lookupType (schema (buildColumn t c f))
{ fst := c, snd := Schema.colImpliesName (Schema.hasAppendedHead ss c τ []) } =
τ
t : Table (s :: ss)
f : Row (s :: ss) → Option τ
⊢ Row ss → Option τ | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | buildColumn_spec4 | [115, 1] | [127, 36] | exact (dropColumn t _) | case cons.t
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst✝ : DecidableEq τ
c : η
s : Header
ss : List Header
ih :
∀ (t : Table ss) (f : Row ss → Option τ),
Schema.lookupType (schema (buildColumn t c f))
{ fst := c, snd := Schema.colImpliesName (Schema.hasAppendedHead ss c τ []) } =
τ
t : Table (s :: ss)
f : Row (s :: ss) → Option τ
⊢ Table ss | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | buildColumn_spec4 | [115, 1] | [127, 36] | exact f ∘ (Row.cons Cell.emp) | case cons.f
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
inst✝ : DecidableEq τ
c : η
s : Header
ss : List Header
ih :
∀ (t : Table ss) (f : Row ss → Option τ),
Schema.lookupType (schema (buildColumn t c f))
{ fst := c, snd := Schema.colImpliesName (Schema.hasAppendedHead ss c τ []) } =
τ
t : Table (s :: ss)
f : Row (s :: ss) → Option τ
⊢ Row ss → Option τ | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | buildColumn_spec5 | [129, 1] | [136, 25] | intros τ t c f | η : Type u_η
dec_η : DecidableEq η
sch : Schema
⊢ ∀ {τ : Type u} (t : Table sch) (c : η) (f : Row sch → Option τ), nrows (buildColumn t c f) = nrows t | η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
t : Table sch
c : η
f : Row sch → Option τ
⊢ nrows (buildColumn t c f) = nrows t |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | buildColumn_spec5 | [129, 1] | [136, 25] | simp only [nrows, buildColumn, addColumn, Schema.length_eq_List_length] | η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
t : Table sch
c : η
f : Row sch → Option τ
⊢ nrows (buildColumn t c f) = nrows t | η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
t : Table sch
c : η
f : Row sch → Option τ
⊢ List.length (List.map (fun x => Row.addColumn x.fst c x.snd) (List.zip t.rows (List.map f t.rows))) =
List.length t.rows |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | buildColumn_spec5 | [129, 1] | [136, 25] | rw [List.length_map, List.zip_length_eq_of_length_eq] | η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
t : Table sch
c : η
f : Row sch → Option τ
⊢ List.length (List.map (fun x => Row.addColumn x.fst c x.snd) (List.zip t.rows (List.map f t.rows))) =
List.length t.rows | case h
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
t : Table sch
c : η
f : Row sch → Option τ
⊢ List.length t.rows = List.length (List.map f t.rows) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | buildColumn_spec5 | [129, 1] | [136, 25] | apply Eq.symm | case h
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
t : Table sch
c : η
f : Row sch → Option τ
⊢ List.length t.rows = List.length (List.map f t.rows) | case h.h
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
t : Table sch
c : η
f : Row sch → Option τ
⊢ List.length (List.map f t.rows) = List.length t.rows |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | buildColumn_spec5 | [129, 1] | [136, 25] | apply List.length_map | case h.h
η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
t : Table sch
c : η
f : Row sch → Option τ
⊢ List.length (List.map f t.rows) = List.length t.rows | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | vcat_spec2 | [145, 1] | [150, 43] | intro t1 t2 | η : Type u_η
dec_η : DecidableEq η
sch : Schema
⊢ ∀ (t1 t2 : Table sch), nrows (vcat t1 t2) = nrows t1 + nrows t2 | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t1 t2 : Table sch
⊢ nrows (vcat t1 t2) = nrows t1 + nrows t2 |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | vcat_spec2 | [145, 1] | [150, 43] | simp only [nrows, Schema.length_eq_List_length] | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t1 t2 : Table sch
⊢ nrows (vcat t1 t2) = nrows t1 + nrows t2 | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t1 t2 : Table sch
⊢ List.length (vcat t1 t2).rows = List.length t1.rows + List.length t2.rows |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | vcat_spec2 | [145, 1] | [150, 43] | exact List.length_append t1.rows t2.rows | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t1 t2 : Table sch
⊢ List.length (vcat t1 t2).rows = List.length t1.rows + List.length t2.rows | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | hcat_spec2 | [160, 1] | [166, 47] | intros sch₁ sch₂ t₁ t₂ h | η : Type u_η
dec_η : DecidableEq η
sch : Schema
⊢ ∀ {sch₁ sch₂ : Schema} (t₁ : Table sch₁) (t₂ : Table sch₂), nrows t₁ = nrows t₂ → nrows (hcat t₁ t₂) = nrows t₁ | η : Type u_η
dec_η : DecidableEq η
sch : Schema
sch₁ sch₂ : Schema
t₁ : Table sch₁
t₂ : Table sch₂
h : nrows t₁ = nrows t₂
⊢ nrows (hcat t₁ t₂) = nrows t₁ |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | hcat_spec2 | [160, 1] | [166, 47] | simp only [nrows, hcat, Schema.length_eq_List_length] at * | η : Type u_η
dec_η : DecidableEq η
sch : Schema
sch₁ sch₂ : Schema
t₁ : Table sch₁
t₂ : Table sch₂
h : nrows t₁ = nrows t₂
⊢ nrows (hcat t₁ t₂) = nrows t₁ | η : Type u_η
dec_η : DecidableEq η
sch : Schema
sch₁ sch₂ : Schema
t₁ : Table sch₁
t₂ : Table sch₂
h : List.length t₁.rows = List.length t₂.rows
⊢ List.length (List.map (fun x => Row.append x.fst x.snd) (List.zip t₁.rows t₂.rows)) = List.length t₁.rows |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | hcat_spec2 | [160, 1] | [166, 47] | rw [List.length_map] | η : Type u_η
dec_η : DecidableEq η
sch : Schema
sch₁ sch₂ : Schema
t₁ : Table sch₁
t₂ : Table sch₂
h : List.length t₁.rows = List.length t₂.rows
⊢ List.length (List.map (fun x => Row.append x.fst x.snd) (List.zip t₁.rows t₂.rows)) = List.length t₁.rows | η : Type u_η
dec_η : DecidableEq η
sch : Schema
sch₁ sch₂ : Schema
t₁ : Table sch₁
t₂ : Table sch₂
h : List.length t₁.rows = List.length t₂.rows
⊢ List.length (List.zip t₁.rows t₂.rows) = List.length t₁.rows |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | hcat_spec2 | [160, 1] | [166, 47] | apply List.zip_length_eq_of_length_eq _ _ h | η : Type u_η
dec_η : DecidableEq η
sch : Schema
sch₁ sch₂ : Schema
t₁ : Table sch₁
t₂ : Table sch₂
h : List.length t₁.rows = List.length t₂.rows
⊢ List.length (List.zip t₁.rows t₂.rows) = List.length t₁.rows | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | crossJoin_spec2 | [186, 1] | [191, 26] | intros sch₁ sch₂ t₁ t₂ | η : Type u_η
dec_η : DecidableEq η
sch : Schema
⊢ ∀ {sch₁ sch₂ : Schema} (t₁ : Table sch₁) (t₂ : Table sch₂), nrows (crossJoin t₁ t₂) = nrows t₁ * nrows t₂ | η : Type u_η
dec_η : DecidableEq η
sch : Schema
sch₁ sch₂ : Schema
t₁ : Table sch₁
t₂ : Table sch₂
⊢ nrows (crossJoin t₁ t₂) = nrows t₁ * nrows t₂ |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | crossJoin_spec2 | [186, 1] | [191, 26] | simp only [nrows, crossJoin, List.length_map, Schema.length_eq_List_length] | η : Type u_η
dec_η : DecidableEq η
sch : Schema
sch₁ sch₂ : Schema
t₁ : Table sch₁
t₂ : Table sch₂
⊢ nrows (crossJoin t₁ t₂) = nrows t₁ * nrows t₂ | η : Type u_η
dec_η : DecidableEq η
sch : Schema
sch₁ sch₂ : Schema
t₁ : Table sch₁
t₂ : Table sch₂
⊢ List.length (List.prod t₁.rows t₂.rows) = List.length t₁.rows * List.length t₂.rows |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | crossJoin_spec2 | [186, 1] | [191, 26] | apply List.length_prod | η : Type u_η
dec_η : DecidableEq η
sch : Schema
sch₁ sch₂ : Schema
t₁ : Table sch₁
t₂ : Table sch₂
⊢ List.length (List.prod t₁.rows t₂.rows) = List.length t₁.rows * List.length t₂.rows | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | getColumn1_spec1 | [254, 1] | [259, 24] | intro t n h | η : Type u_η
dec_η : DecidableEq η
sch : Schema
⊢ ∀ (t : Table sch) (n : Nat) (h : n < ncols t), List.length (getColumn1 t n) = nrows t | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
n : Nat
h : n < ncols t
⊢ List.length (getColumn1 t n) = nrows t |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | getColumn1_spec1 | [254, 1] | [259, 24] | simp only [getColumn1, nrows, Schema.length_eq_List_length] | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
n : Nat
h : n < ncols t
⊢ List.length (getColumn1 t n) = nrows t | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
n : Nat
h : n < ncols t
⊢ List.length (List.map (fun r => Cell.toOption (Row.nth r n h)) t.rows) = List.length t.rows |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | getColumn1_spec1 | [254, 1] | [259, 24] | apply List.length_map | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
n : Nat
h : n < ncols t
⊢ List.length (List.map (fun r => Cell.toOption (Row.nth r n h)) t.rows) = List.length t.rows | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | getColumn2_spec2 | [267, 1] | [272, 24] | intro τ t c h | η : Type u_η
dec_η : DecidableEq η
sch : Schema
⊢ ∀ {τ : Type u} (t : Table sch) (c : η) (h : Schema.HasCol (c, τ) sch), List.length (getColumn2 t c) = nrows t | η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
t : Table sch
c : η
h : Schema.HasCol (c, τ) sch
⊢ List.length (getColumn2 t c) = nrows t |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | getColumn2_spec2 | [267, 1] | [272, 24] | simp only [getColumn2, nrows, Schema.length_eq_List_length] | η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
t : Table sch
c : η
h : Schema.HasCol (c, τ) sch
⊢ List.length (getColumn2 t c) = nrows t | η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
t : Table sch
c : η
h : Schema.HasCol (c, τ) sch
⊢ List.length (List.map (fun r => getValue r c) t.rows) = List.length t.rows |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | getColumn2_spec2 | [267, 1] | [272, 24] | apply List.length_map | η : Type u_η
dec_η : DecidableEq η
sch : Schema
τ : Type u
t : Table sch
c : η
h : Schema.HasCol (c, τ) sch
⊢ List.length (List.map (fun r => getValue r c) t.rows) = List.length t.rows | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | selectRows1_spec2 | [282, 1] | [287, 24] | intro t ns | η : Type u_η
dec_η : DecidableEq η
sch : Schema
⊢ ∀ (t : Table sch) (ns : List (Fin (nrows t))), nrows (selectRows1 t ns) = List.length ns | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
ns : List (Fin (nrows t))
⊢ nrows (selectRows1 t ns) = List.length ns |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | selectRows1_spec2 | [282, 1] | [287, 24] | rw [selectRows1, nrows, Schema.length_eq_List_length] | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
ns : List (Fin (nrows t))
⊢ nrows (selectRows1 t ns) = List.length ns | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
ns : List (Fin (nrows t))
⊢ List.length { rows := List.map (fun n => getRow t n.val) ns }.rows = List.length ns |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | selectRows1_spec2 | [282, 1] | [287, 24] | apply List.length_map | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
ns : List (Fin (nrows t))
⊢ List.length { rows := List.map (fun n => getRow t n.val) ns }.rows = List.length ns | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | selectRows2_spec2 | [296, 1] | [304, 10] | intro t bs h | η : Type u_η
dec_η : DecidableEq η
sch : Schema
⊢ ∀ (t : Table sch) (bs : List Bool),
List.length bs = nrows t → nrows (selectRows2 t bs) = List.length (List.removeAllEq bs [false]) | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
bs : List Bool
h : List.length bs = nrows t
⊢ nrows (selectRows2 t bs) = List.length (List.removeAllEq bs [false]) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | selectRows2_spec2 | [296, 1] | [304, 10] | simp only [nrows, selectRows2, Schema.length_eq_List_length] | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
bs : List Bool
h : List.length bs = nrows t
⊢ nrows (selectRows2 t bs) = List.length (List.removeAllEq bs [false]) | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
bs : List Bool
h : List.length bs = nrows t
⊢ List.length (List.sieve bs t.rows) = List.length (List.removeAllEq bs [false]) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | selectRows2_spec2 | [296, 1] | [304, 10] | apply List.sieve_removeAllEq | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
bs : List Bool
h : List.length bs = nrows t
⊢ List.length (List.sieve bs t.rows) = List.length (List.removeAllEq bs [false]) | case a
η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
bs : List Bool
h : List.length bs = nrows t
⊢ List.length bs = List.length t.rows |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | selectRows2_spec2 | [296, 1] | [304, 10] | rw [nrows, Schema.length_eq_List_length] at h | case a
η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
bs : List Bool
h : List.length bs = nrows t
⊢ List.length bs = List.length t.rows | case a
η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
bs : List Bool
h : List.length bs = List.length t.rows
⊢ List.length bs = List.length t.rows |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | selectRows2_spec2 | [296, 1] | [304, 10] | exact h | case a
η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
bs : List Bool
h : List.length bs = List.length t.rows
⊢ List.length bs = List.length t.rows | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | selectColumns1_spec1 | [308, 1] | [313, 77] | intro t bs | η : Type u_η
dec_η : DecidableEq η
sch : Schema
⊢ ∀ (t : Table sch) (bs : List Bool), header (selectColumns1 t bs) <+ header t | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
bs : List Bool
⊢ header (selectColumns1 t bs) <+ header t |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | selectColumns1_spec1 | [308, 1] | [313, 77] | simp only [header, Schema.names, Schema.sieve_eq_List_sieve] | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
bs : List Bool
⊢ header (selectColumns1 t bs) <+ header t | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
bs : List Bool
⊢ List.map Prod.fst (List.sieve bs sch) <+ List.map Prod.fst sch |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | selectColumns1_spec1 | [308, 1] | [313, 77] | exact List.sublist_of_map_sublist _ _ Prod.fst $ List.sieve_sublist bs sch | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
bs : List Bool
⊢ List.map Prod.fst (List.sieve bs sch) <+ List.map Prod.fst sch | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | ncols_eq_header_length | [316, 1] | [321, 24] | intro t | η : Type u_η
dec_η : DecidableEq η
sch : Schema
⊢ ∀ (t : Table sch), ncols t = List.length (header t) | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
⊢ ncols t = List.length (header t) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | ncols_eq_header_length | [316, 1] | [321, 24] | simp only [ncols, Schema.length_eq_List_length] | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
⊢ ncols t = List.length (header t) | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
⊢ List.length sch = List.length (header t) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | ncols_eq_header_length | [316, 1] | [321, 24] | apply Eq.symm | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
⊢ List.length sch = List.length (header t) | case h
η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
⊢ List.length (header t) = List.length sch |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | ncols_eq_header_length | [316, 1] | [321, 24] | apply List.length_map | case h
η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
⊢ List.length (header t) = List.length sch | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | selectColumns1_spec2 | [323, 1] | [332, 37] | simp only [header, Schema.sieve_eq_List_sieve] | η : Type u_η
dec_η : DecidableEq η
sch : Schema
hu : Schema.Unique sch
t : Table sch
bs : List Bool
h : List.length bs = ncols t
i : Nat
hlt : i < ncols t
⊢ List.get (header t) { val := i, isLt := (_ : i < List.length (header t)) } ∈ header (selectColumns1 t bs) ↔
List.get bs { val := i, isLt := (_ : i < List.length bs) } = true | η : Type u_η
dec_η : DecidableEq η
sch : Schema
hu : Schema.Unique sch
t : Table sch
bs : List Bool
h : List.length bs = ncols t
i : Nat
hlt : i < ncols t
⊢ List.get (Schema.names sch) { val := i, isLt := (_ : i < List.length (header t)) } ∈
Schema.names (List.sieve bs sch) ↔
List.get bs { val := i, isLt := (_ : i < List.length bs) } = true |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | selectColumns1_spec2 | [323, 1] | [332, 37] | exact List.sieve_map_mem_iff_true_unique (Schema.length_eq_List_length ▸ hlt)
(h.symm ▸ hlt) Prod.fst hu | η : Type u_η
dec_η : DecidableEq η
sch : Schema
hu : Schema.Unique sch
t : Table sch
bs : List Bool
h : List.length bs = ncols t
i : Nat
hlt : i < ncols t
⊢ List.get (Schema.names sch) { val := i, isLt := (_ : i < List.length (header t)) } ∈
Schema.names (List.sieve bs sch) ↔
List.get bs { val := i, isLt := (_ : i < List.length bs) } = true | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | selectColumns1_spec3 | [334, 1] | [339, 27] | simp only [schema, Schema.sieve_eq_List_sieve] | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
bs : List Bool
⊢ schema (selectColumns1 t bs) <+ schema t | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
bs : List Bool
⊢ List.sieve bs sch <+ sch |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | selectColumns1_spec3 | [334, 1] | [339, 27] | apply List.sieve_sublist | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
bs : List Bool
⊢ List.sieve bs sch <+ sch | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | selectColumns1_spec4 | [341, 1] | [346, 24] | intro t bs | η : Type u_η
dec_η : DecidableEq η
sch : Schema
⊢ ∀ (t : Table sch) (bs : List Bool), nrows (selectColumns1 t bs) = nrows t | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
bs : List Bool
⊢ nrows (selectColumns1 t bs) = nrows t |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | selectColumns1_spec4 | [341, 1] | [346, 24] | simp only [nrows, selectColumns1, Schema.length_eq_List_length] | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
bs : List Bool
⊢ nrows (selectColumns1 t bs) = nrows t | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
bs : List Bool
⊢ List.length (List.map (fun r => Row.sieve bs r) t.rows) = List.length t.rows |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | selectColumns1_spec4 | [341, 1] | [346, 24] | apply List.length_map | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
bs : List Bool
⊢ List.length (List.map (fun r => Row.sieve bs r) t.rows) = List.length t.rows | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | selectColumns2_spec1 | [350, 1] | [356, 24] | intro t ns | η : Type u_η
dec_η : DecidableEq η
sch : Schema
⊢ ∀ (t : Table sch) (ns : List (Fin (ncols t))), ncols (selectColumns2 t ns) = List.length ns | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
ns : List (Fin (ncols t))
⊢ ncols (selectColumns2 t ns) = List.length ns |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | selectColumns2_spec1 | [350, 1] | [356, 24] | simp only [ncols, Schema.length_eq_List_length, Schema.nths,
Schema.map_eq_List_map] | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
ns : List (Fin (ncols t))
⊢ ncols (selectColumns2 t ns) = List.length ns | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
ns : List (Fin (ncols t))
⊢ List.length (List.map (fun n => Schema.nth sch n.val (_ : n.val < Schema.length sch)) ns) = List.length ns |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | selectColumns2_spec1 | [350, 1] | [356, 24] | apply List.length_map | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
ns : List (Fin (ncols t))
⊢ List.length (List.map (fun n => Schema.nth sch n.val (_ : n.val < Schema.length sch)) ns) = List.length ns | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | selectColumns2_spec2 | [363, 1] | [373, 39] | intro t ns i hi | η : Type u_η
dec_η : DecidableEq η
sch : Schema
⊢ ∀ (t : Table sch) (ns : List (Fin (ncols t))) (i : Nat) (hi : i < List.length ns),
List.get (header (selectColumns2 t ns)) { val := i, isLt := (_ : i < List.length (header (selectColumns2 t ns))) } =
List.get (header t) (finHeaderLengthOfFinNcols t (List.get ns { val := i, isLt := hi })) | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
ns : List (Fin (ncols t))
i : Nat
hi : i < List.length ns
⊢ List.get (header (selectColumns2 t ns)) { val := i, isLt := (_ : i < List.length (header (selectColumns2 t ns))) } =
List.get (header t) (finHeaderLengthOfFinNcols t (List.get ns { val := i, isLt := hi })) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | selectColumns2_spec2 | [363, 1] | [373, 39] | simp only [header] | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
ns : List (Fin (ncols t))
i : Nat
hi : i < List.length ns
⊢ List.get (header (selectColumns2 t ns)) { val := i, isLt := (_ : i < List.length (header (selectColumns2 t ns))) } =
List.get (header t) (finHeaderLengthOfFinNcols t (List.get ns { val := i, isLt := hi })) | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
ns : List (Fin (ncols t))
i : Nat
hi : i < List.length ns
⊢ List.get (Schema.names (Schema.nths sch ns))
{ val := i, isLt := (_ : i < List.length (header (selectColumns2 t ns))) } =
List.get (Schema.names sch) (finHeaderLengthOfFinNcols t (List.get ns { val := i, isLt := hi })) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | selectColumns2_spec2 | [363, 1] | [373, 39] | simp only [finHeaderLengthOfFinNcols] | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
ns : List (Fin (ncols t))
i : Nat
hi : i < List.length ns
⊢ List.get (Schema.names (Schema.nths sch ns))
{ val := i, isLt := (_ : i < List.length (header (selectColumns2 t ns))) } =
List.get (Schema.names sch) (finHeaderLengthOfFinNcols t (List.get ns { val := i, isLt := hi })) | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
ns : List (Fin (ncols t))
i : Nat
hi : i < List.length ns
⊢ List.get (Schema.names (Schema.nths sch ns))
{ val := i, isLt := (_ : i < List.length (header (selectColumns2 t ns))) } =
List.get (Schema.names sch)
{ val := (List.get ns { val := i, isLt := hi }).val,
isLt := (_ : (List.get ns { val := i, isLt := hi }).val < List.length (header t)) } |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | selectColumns2_spec2 | [363, 1] | [373, 39] | apply Schema.get_map_nths_eq_get_get | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
ns : List (Fin (ncols t))
i : Nat
hi : i < List.length ns
⊢ List.get (Schema.names (Schema.nths sch ns))
{ val := i, isLt := (_ : i < List.length (header (selectColumns2 t ns))) } =
List.get (Schema.names sch)
{ val := (List.get ns { val := i, isLt := hi }).val,
isLt := (_ : (List.get ns { val := i, isLt := hi }).val < List.length (header t)) } | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | selectColumns2_spec3 | [375, 1] | [383, 45] | intro sch t ns c | η : Type u_η
dec_η : DecidableEq η
sch : Schema
⊢ ∀ {sch : Schema} (t : Table sch) (ns : List (Fin (ncols t))) (c : CertifiedName (schema (selectColumns2 t ns))),
Schema.lookupType (schema (selectColumns2 t ns)) c =
Schema.lookupType (schema t) { fst := c.fst, snd := Schema.hasNameOfNthsHasName c.snd } | η : Type u_η
dec_η : DecidableEq η
sch✝ : Schema
sch : Schema
t : Table sch
ns : List (Fin (ncols t))
c : CertifiedName (schema (selectColumns2 t ns))
⊢ Schema.lookupType (schema (selectColumns2 t ns)) c =
Schema.lookupType (schema t) { fst := c.fst, snd := Schema.hasNameOfNthsHasName c.snd } |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | selectColumns2_spec3 | [375, 1] | [383, 45] | unfold schema at * | η : Type u_η
dec_η : DecidableEq η
sch✝ : Schema
sch : Schema
t : Table sch
ns : List (Fin (ncols t))
c : CertifiedName (schema (selectColumns2 t ns))
⊢ Schema.lookupType (schema (selectColumns2 t ns)) c =
Schema.lookupType (schema t) { fst := c.fst, snd := Schema.hasNameOfNthsHasName c.snd } | η : Type u_η
dec_η : DecidableEq η
sch✝ : Schema
sch : Schema
t : Table sch
ns : List (Fin (ncols t))
c : CertifiedName (Schema.nths sch ns)
⊢ Schema.lookupType (Schema.nths sch ns) c =
Schema.lookupType sch { fst := c.fst, snd := Schema.hasNameOfNthsHasName c.snd } |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | selectColumns2_spec3 | [375, 1] | [383, 45] | apply Schema.lookupType_nths_eq_lookupType | η : Type u_η
dec_η : DecidableEq η
sch✝ : Schema
sch : Schema
t : Table sch
ns : List (Fin (ncols t))
c : CertifiedName (Schema.nths sch ns)
⊢ Schema.lookupType (Schema.nths sch ns) c =
Schema.lookupType sch { fst := c.fst, snd := Schema.hasNameOfNthsHasName c.snd } | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/Proofs.lean | selectColumns2_spec4 | [385, 1] | [390, 24] | intro t ns | η : Type u_η
dec_η : DecidableEq η
sch : Schema
⊢ ∀ (t : Table sch) (ns : List (Fin (ncols t))), nrows (selectColumns2 t ns) = nrows t | η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
ns : List (Fin (ncols t))
⊢ nrows (selectColumns2 t ns) = nrows t |
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