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/BuiltinExtensions.lean | List.mem_fst_matchKey_key_or_snd | [1373, 1] | [1418, 25] | cases ih with
| inl => contradiction
| inr hmem => exact hmem | case inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkeq : k' = k
this : x ∈ map Prod.fst ys
ih : x = k ∨ x ∈ map Prod.fst (matchKey ys k).snd
⊢ x ∈ map Prod.fst (matchKey ys k).snd | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_matchKey_key_or_snd | [1373, 1] | [1418, 25] | cases hx with
| head => contradiction
| tail => assumption | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkeq : k' = k
⊢ x ∈ map Prod.fst ys | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_matchKey_key_or_snd | [1373, 1] | [1418, 25] | contradiction | case head
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
k k' : κ
v : ν
ys : List (κ × ν)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkeq : k' = k
h : ¬(k', v).fst = k
⊢ (k', v).fst ∈ map Prod.fst ys | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_matchKey_key_or_snd | [1373, 1] | [1418, 25] | assumption | case tail
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkeq : k' = k
a✝ : Mem x (map Prod.fst ys)
⊢ x ∈ map Prod.fst ys | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_matchKey_key_or_snd | [1373, 1] | [1418, 25] | contradiction | case inl.inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkeq : k' = k
this : x ∈ map Prod.fst ys
h✝ : x = k
⊢ x ∈ map Prod.fst (matchKey ys k).snd | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_matchKey_key_or_snd | [1373, 1] | [1418, 25] | exact hmem | case inl.inr
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkeq : k' = k
this : x ∈ map Prod.fst ys
hmem : x ∈ map Prod.fst (matchKey ys k).snd
⊢ x ∈ map Prod.fst (matchKey ys k).snd | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_matchKey_key_or_snd | [1373, 1] | [1418, 25] | simp only [hkneq, ite_false] | case inr
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
⊢ x ∈
map Prod.fst
(if k' = k then (v :: (matchKey ys k).fst, (matchKey ys k).snd)
else ((matchKey ys k).fst, (k', v) :: (matchKey ys k).snd)).snd | case inr
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
⊢ x ∈ map Prod.fst ((k', v) :: (matchKey ys k).snd) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_matchKey_key_or_snd | [1373, 1] | [1418, 25] | simp only [map] | case inr
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
⊢ x ∈ map Prod.fst ((k', v) :: (matchKey ys k).snd) | case inr
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
⊢ x ∈ k' :: map Prod.fst (matchKey ys k).snd |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_matchKey_key_or_snd | [1373, 1] | [1418, 25] | cases Decidable.em (x = k') with
| inl hxeq => rw [hxeq]; apply Mem.head
| inr hxneq =>
apply Mem.tail
have : x ∈ map Prod.fst (matchKey ys k).snd := by
cases hx with
| head => contradiction
| tail _ htail =>
have := mem_fst_matchKey_key_or_snd htail k
cases this with
| inl => contradiction
| inr => assumption
have ih := mem_fst_matchKey_key_or_snd this k'
cases ih with
| inl => contradiction
| inr => assumption | case inr
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
⊢ x ∈ k' :: map Prod.fst (matchKey ys k).snd | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_matchKey_key_or_snd | [1373, 1] | [1418, 25] | rw [hxeq] | case inr.inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxeq : x = k'
⊢ x ∈ k' :: map Prod.fst (matchKey ys k).snd | case inr.inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxeq : x = k'
⊢ k' ∈ k' :: map Prod.fst (matchKey ys k).snd |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_matchKey_key_or_snd | [1373, 1] | [1418, 25] | apply Mem.head | case inr.inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxeq : x = k'
⊢ k' ∈ k' :: map Prod.fst (matchKey ys k).snd | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_matchKey_key_or_snd | [1373, 1] | [1418, 25] | apply Mem.tail | case inr.inr
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxneq : ¬x = k'
⊢ x ∈ k' :: map Prod.fst (matchKey ys k).snd | case inr.inr.a
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxneq : ¬x = k'
⊢ Mem x (map Prod.fst (matchKey ys k).snd) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_matchKey_key_or_snd | [1373, 1] | [1418, 25] | have : x ∈ map Prod.fst (matchKey ys k).snd := by
cases hx with
| head => contradiction
| tail _ htail =>
have := mem_fst_matchKey_key_or_snd htail k
cases this with
| inl => contradiction
| inr => assumption | case inr.inr.a
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxneq : ¬x = k'
⊢ Mem x (map Prod.fst (matchKey ys k).snd) | case inr.inr.a
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxneq : ¬x = k'
this : x ∈ map Prod.fst (matchKey ys k).snd
⊢ Mem x (map Prod.fst (matchKey ys k).snd) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_matchKey_key_or_snd | [1373, 1] | [1418, 25] | have ih := mem_fst_matchKey_key_or_snd this k' | case inr.inr.a
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxneq : ¬x = k'
this : x ∈ map Prod.fst (matchKey ys k).snd
⊢ Mem x (map Prod.fst (matchKey ys k).snd) | case inr.inr.a
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxneq : ¬x = k'
this : x ∈ map Prod.fst (matchKey ys k).snd
ih : x = k' ∨ x ∈ map Prod.fst (matchKey (matchKey ys k).snd k').snd
⊢ Mem x (map Prod.fst (matchKey ys k).snd) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_matchKey_key_or_snd | [1373, 1] | [1418, 25] | cases ih with
| inl => contradiction
| inr => assumption | case inr.inr.a
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxneq : ¬x = k'
this : x ∈ map Prod.fst (matchKey ys k).snd
ih : x = k' ∨ x ∈ map Prod.fst (matchKey (matchKey ys k).snd k').snd
⊢ Mem x (map Prod.fst (matchKey ys k).snd) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_matchKey_key_or_snd | [1373, 1] | [1418, 25] | cases hx with
| head => contradiction
| tail _ htail =>
have := mem_fst_matchKey_key_or_snd htail k
cases this with
| inl => contradiction
| inr => assumption | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxneq : ¬x = k'
⊢ x ∈ map Prod.fst (matchKey ys k).snd | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_matchKey_key_or_snd | [1373, 1] | [1418, 25] | contradiction | case head
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
k k' : κ
v : ν
ys : List (κ × ν)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
h : ¬(k', v).fst = k
hxneq : ¬(k', v).fst = k'
⊢ (k', v).fst ∈ map Prod.fst (matchKey ys k).snd | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_matchKey_key_or_snd | [1373, 1] | [1418, 25] | have := mem_fst_matchKey_key_or_snd htail k | case tail
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxneq : ¬x = k'
htail : Mem x (map Prod.fst ys)
⊢ x ∈ map Prod.fst (matchKey ys k).snd | case tail
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxneq : ¬x = k'
htail : Mem x (map Prod.fst ys)
this : x = k ∨ x ∈ map Prod.fst (matchKey ys k).snd
⊢ x ∈ map Prod.fst (matchKey ys k).snd |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_matchKey_key_or_snd | [1373, 1] | [1418, 25] | cases this with
| inl => contradiction
| inr => assumption | case tail
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxneq : ¬x = k'
htail : Mem x (map Prod.fst ys)
this : x = k ∨ x ∈ map Prod.fst (matchKey ys k).snd
⊢ x ∈ map Prod.fst (matchKey ys k).snd | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_matchKey_key_or_snd | [1373, 1] | [1418, 25] | contradiction | case tail.inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxneq : ¬x = k'
htail : Mem x (map Prod.fst ys)
h✝ : x = k
⊢ x ∈ map Prod.fst (matchKey ys k).snd | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_matchKey_key_or_snd | [1373, 1] | [1418, 25] | assumption | case tail.inr
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxneq : ¬x = k'
htail : Mem x (map Prod.fst ys)
h✝ : x ∈ map Prod.fst (matchKey ys k).snd
⊢ x ∈ map Prod.fst (matchKey ys k).snd | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_matchKey_key_or_snd | [1373, 1] | [1418, 25] | contradiction | case inr.inr.a.inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxneq : ¬x = k'
this : x ∈ map Prod.fst (matchKey ys k).snd
h✝ : x = k'
⊢ Mem x (map Prod.fst (matchKey ys k).snd) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_matchKey_key_or_snd | [1373, 1] | [1418, 25] | assumption | case inr.inr.a.inr
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxneq : ¬x = k'
this : x ∈ map Prod.fst (matchKey ys k).snd
h✝ : x ∈ map Prod.fst (matchKey (matchKey ys k).snd k').snd
⊢ Mem x (map Prod.fst (matchKey ys k).snd) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_matchKey_key_or_snd | [1373, 1] | [1418, 25] | assumption | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
_x✝ : (ys : List (κ × ν)) ×' (x : κ) ×' (_ : x ∈ map Prod.fst ys) ×' κ
a✝³ :
∀ (y : (ys : List (κ × ν)) ×' (x : κ) ×' (_ : x ∈ map Prod.fst ys) ×' κ),
(invImage
(fun a =>
PSigma.casesOn a fun ys snd => PSigma.casesOn snd fun x snd => PSigma.casesOn snd fun hx snd => length ys)
instWellFoundedRelation).1
y _x✝ →
y.2.1 = y.2.2.2 ∨ y.2.1 ∈ map Prod.fst (matchKey y.1 y.2.2.2).snd
ys✝ : List (κ × ν)
x✝¹ : (x : κ) ×' (_ : x ∈ map Prod.fst ys✝) ×' κ
a✝² :
∀ (y : (ys : List (κ × ν)) ×' (x : κ) ×' (_ : x ∈ map Prod.fst ys) ×' κ),
(invImage
(fun a =>
PSigma.casesOn a fun ys snd => PSigma.casesOn snd fun x snd => PSigma.casesOn snd fun hx snd => length ys)
instWellFoundedRelation).1
y { fst := ys✝, snd := x✝¹ } →
y.2.1 = y.2.2.2 ∨ y.2.1 ∈ map Prod.fst (matchKey y.1 y.2.2.2).snd
x : κ
hx✝¹ : (_ : x ∈ map Prod.fst ys✝) ×' κ
a✝¹ :
∀ (y : (ys : List (κ × ν)) ×' (x : κ) ×' (_ : x ∈ map Prod.fst ys) ×' κ),
(invImage
(fun a =>
PSigma.casesOn a fun ys snd => PSigma.casesOn snd fun x snd => PSigma.casesOn snd fun hx snd => length ys)
instWellFoundedRelation).1
y { fst := ys✝, snd := { fst := x, snd := hx✝¹ } } →
y.2.1 = y.2.2.2 ∨ y.2.1 ∈ map Prod.fst (matchKey y.1 y.2.2.2).snd
hx✝ : x ∈ map Prod.fst ys✝
k : κ
a✝ :
∀ (y : (ys : List (κ × ν)) ×' (x : κ) ×' (_ : x ∈ map Prod.fst ys) ×' κ),
(invImage
(fun a =>
PSigma.casesOn a fun ys snd => PSigma.casesOn snd fun x snd => PSigma.casesOn snd fun hx snd => length ys)
instWellFoundedRelation).1
y { fst := ys✝, snd := { fst := x, snd := { fst := hx✝, snd := k } } } →
y.2.1 = y.2.2.2 ∨ y.2.1 ∈ map Prod.fst (matchKey y.1 y.2.2.2).snd
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
x✝ :
∀ (y : (ys : List (κ × ν)) ×' (x : κ) ×' (_ : x ∈ map Prod.fst ys) ×' κ),
(invImage
(fun a =>
PSigma.casesOn a fun ys snd => PSigma.casesOn snd fun x snd => PSigma.casesOn snd fun hx snd => length ys)
instWellFoundedRelation).1
y { fst := (k', v) :: ys, snd := { fst := x, snd := { fst := hx, snd := k } } } →
y.2.1 = y.2.2.2 ∨ y.2.1 ∈ map Prod.fst (matchKey y.1 y.2.2.2).snd
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
h✝³ : (_ : k' = k ∨ ¬k' = k) = (_ : k' = k ∨ ¬k' = k)
hxneq : ¬x = k'
h✝² : (_ : x = k' ∨ ¬x = k') = (_ : x = k' ∨ ¬x = k')
b✝ : κ
as✝ : List κ
htail✝ : Mem x as✝
h✝¹ : map Prod.fst ((k', v) :: ys) = b✝ :: as✝
head_eq✝ : (k', v).fst = b✝
tail_eq✝ : map Prod.fst ys = as✝
htail : Mem x (map Prod.fst ys)
h✝ : HEq hx (_ : Mem x ((k', v).fst :: map Prod.fst ys))
⊢ (invImage
(fun a =>
PSigma.casesOn a fun ys snd => PSigma.casesOn snd fun x snd => PSigma.casesOn snd fun hx snd => length ys)
instWellFoundedRelation).1
{ fst := ys, snd := { fst := x, snd := { fst := htail, snd := k } } }
{ fst := (k', v) :: ys, snd := { fst := x, snd := { fst := hx, snd := k } } } | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_groupByKey_key_or_snd | [1421, 1] | [1468, 25] | simp only [matchKey] | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
⊢ x ∈ map Prod.fst (groupByKey (matchKey ((k', v) :: ys) k).snd) | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
⊢ x ∈
map Prod.fst
(groupByKey
(if k' = k then (v :: (matchKey ys k).fst, (matchKey ys k).snd)
else ((matchKey ys k).fst, (k', v) :: (matchKey ys k).snd)).snd) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_groupByKey_key_or_snd | [1421, 1] | [1468, 25] | cases Decidable.em (k' = k) with
| inl hkeq =>
simp only [hkeq, ite_true]
have : x ∈ map Prod.fst ys := by
cases hx with
| head => contradiction
| tail => assumption
have ih := mem_fst_groupByKey_key_or_snd this k
cases ih with
| inl => contradiction
| inr hmem => exact hmem
| inr hkneq =>
simp only [hkneq, ite_false]
simp only [groupByKey]
simp only [map]
cases Decidable.em (x = k') with
| inl hxeq => rw [hxeq]; apply Mem.head
| inr hxneq =>
apply Mem.tail
have : x ∈ map Prod.fst (matchKey ys k).snd := by
cases hx with
| head => contradiction
| tail _ htail =>
have := mem_fst_matchKey_key_or_snd htail k
cases this with
| inl => contradiction
| inr => assumption
have ih := mem_fst_groupByKey_key_or_snd this k'
cases ih with
| inl => contradiction
| inr => assumption | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
⊢ x ∈
map Prod.fst
(groupByKey
(if k' = k then (v :: (matchKey ys k).fst, (matchKey ys k).snd)
else ((matchKey ys k).fst, (k', v) :: (matchKey ys k).snd)).snd) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_groupByKey_key_or_snd | [1421, 1] | [1468, 25] | simp only [hkeq, ite_true] | case inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkeq : k' = k
⊢ x ∈
map Prod.fst
(groupByKey
(if k' = k then (v :: (matchKey ys k).fst, (matchKey ys k).snd)
else ((matchKey ys k).fst, (k', v) :: (matchKey ys k).snd)).snd) | case inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkeq : k' = k
⊢ x ∈ map Prod.fst (groupByKey (matchKey ys k).snd) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_groupByKey_key_or_snd | [1421, 1] | [1468, 25] | have : x ∈ map Prod.fst ys := by
cases hx with
| head => contradiction
| tail => assumption | case inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkeq : k' = k
⊢ x ∈ map Prod.fst (groupByKey (matchKey ys k).snd) | case inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkeq : k' = k
this : x ∈ map Prod.fst ys
⊢ x ∈ map Prod.fst (groupByKey (matchKey ys k).snd) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_groupByKey_key_or_snd | [1421, 1] | [1468, 25] | have ih := mem_fst_groupByKey_key_or_snd this k | case inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkeq : k' = k
this : x ∈ map Prod.fst ys
⊢ x ∈ map Prod.fst (groupByKey (matchKey ys k).snd) | case inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkeq : k' = k
this : x ∈ map Prod.fst ys
ih : x = k ∨ x ∈ map Prod.fst (groupByKey (matchKey ys k).snd)
⊢ x ∈ map Prod.fst (groupByKey (matchKey ys k).snd) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_groupByKey_key_or_snd | [1421, 1] | [1468, 25] | cases ih with
| inl => contradiction
| inr hmem => exact hmem | case inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkeq : k' = k
this : x ∈ map Prod.fst ys
ih : x = k ∨ x ∈ map Prod.fst (groupByKey (matchKey ys k).snd)
⊢ x ∈ map Prod.fst (groupByKey (matchKey ys k).snd) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_groupByKey_key_or_snd | [1421, 1] | [1468, 25] | cases hx with
| head => contradiction
| tail => assumption | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkeq : k' = k
⊢ x ∈ map Prod.fst ys | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_groupByKey_key_or_snd | [1421, 1] | [1468, 25] | contradiction | case head
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
k k' : κ
v : ν
ys : List (κ × ν)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkeq : k' = k
h : ¬(k', v).fst = k
⊢ (k', v).fst ∈ map Prod.fst ys | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_groupByKey_key_or_snd | [1421, 1] | [1468, 25] | assumption | case tail
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkeq : k' = k
a✝ : Mem x (map Prod.fst ys)
⊢ x ∈ map Prod.fst ys | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_groupByKey_key_or_snd | [1421, 1] | [1468, 25] | contradiction | case inl.inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkeq : k' = k
this : x ∈ map Prod.fst ys
h✝ : x = k
⊢ x ∈ map Prod.fst (groupByKey (matchKey ys k).snd) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_groupByKey_key_or_snd | [1421, 1] | [1468, 25] | exact hmem | case inl.inr
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkeq : k' = k
this : x ∈ map Prod.fst ys
hmem : x ∈ map Prod.fst (groupByKey (matchKey ys k).snd)
⊢ x ∈ map Prod.fst (groupByKey (matchKey ys k).snd) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_groupByKey_key_or_snd | [1421, 1] | [1468, 25] | simp only [hkneq, ite_false] | case inr
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
⊢ x ∈
map Prod.fst
(groupByKey
(if k' = k then (v :: (matchKey ys k).fst, (matchKey ys k).snd)
else ((matchKey ys k).fst, (k', v) :: (matchKey ys k).snd)).snd) | case inr
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
⊢ x ∈ map Prod.fst (groupByKey ((k', v) :: (matchKey ys k).snd)) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_groupByKey_key_or_snd | [1421, 1] | [1468, 25] | simp only [groupByKey] | case inr
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
⊢ x ∈ map Prod.fst (groupByKey ((k', v) :: (matchKey ys k).snd)) | case inr
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
⊢ x ∈
map Prod.fst ((k', v :: (matchKey (matchKey ys k).snd k').fst) :: groupByKey (matchKey (matchKey ys k).snd k').snd) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_groupByKey_key_or_snd | [1421, 1] | [1468, 25] | simp only [map] | case inr
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
⊢ x ∈
map Prod.fst ((k', v :: (matchKey (matchKey ys k).snd k').fst) :: groupByKey (matchKey (matchKey ys k).snd k').snd) | case inr
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
⊢ x ∈ k' :: map Prod.fst (groupByKey (matchKey (matchKey ys k).snd k').snd) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_groupByKey_key_or_snd | [1421, 1] | [1468, 25] | cases Decidable.em (x = k') with
| inl hxeq => rw [hxeq]; apply Mem.head
| inr hxneq =>
apply Mem.tail
have : x ∈ map Prod.fst (matchKey ys k).snd := by
cases hx with
| head => contradiction
| tail _ htail =>
have := mem_fst_matchKey_key_or_snd htail k
cases this with
| inl => contradiction
| inr => assumption
have ih := mem_fst_groupByKey_key_or_snd this k'
cases ih with
| inl => contradiction
| inr => assumption | case inr
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
⊢ x ∈ k' :: map Prod.fst (groupByKey (matchKey (matchKey ys k).snd k').snd) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_groupByKey_key_or_snd | [1421, 1] | [1468, 25] | rw [hxeq] | case inr.inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxeq : x = k'
⊢ x ∈ k' :: map Prod.fst (groupByKey (matchKey (matchKey ys k).snd k').snd) | case inr.inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxeq : x = k'
⊢ k' ∈ k' :: map Prod.fst (groupByKey (matchKey (matchKey ys k).snd k').snd) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_groupByKey_key_or_snd | [1421, 1] | [1468, 25] | apply Mem.head | case inr.inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxeq : x = k'
⊢ k' ∈ k' :: map Prod.fst (groupByKey (matchKey (matchKey ys k).snd k').snd) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_groupByKey_key_or_snd | [1421, 1] | [1468, 25] | apply Mem.tail | case inr.inr
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxneq : ¬x = k'
⊢ x ∈ k' :: map Prod.fst (groupByKey (matchKey (matchKey ys k).snd k').snd) | case inr.inr.a
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxneq : ¬x = k'
⊢ Mem x (map Prod.fst (groupByKey (matchKey (matchKey ys k).snd k').snd)) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_groupByKey_key_or_snd | [1421, 1] | [1468, 25] | have : x ∈ map Prod.fst (matchKey ys k).snd := by
cases hx with
| head => contradiction
| tail _ htail =>
have := mem_fst_matchKey_key_or_snd htail k
cases this with
| inl => contradiction
| inr => assumption | case inr.inr.a
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxneq : ¬x = k'
⊢ Mem x (map Prod.fst (groupByKey (matchKey (matchKey ys k).snd k').snd)) | case inr.inr.a
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxneq : ¬x = k'
this : x ∈ map Prod.fst (matchKey ys k).snd
⊢ Mem x (map Prod.fst (groupByKey (matchKey (matchKey ys k).snd k').snd)) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_groupByKey_key_or_snd | [1421, 1] | [1468, 25] | have ih := mem_fst_groupByKey_key_or_snd this k' | case inr.inr.a
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxneq : ¬x = k'
this : x ∈ map Prod.fst (matchKey ys k).snd
⊢ Mem x (map Prod.fst (groupByKey (matchKey (matchKey ys k).snd k').snd)) | case inr.inr.a
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxneq : ¬x = k'
this : x ∈ map Prod.fst (matchKey ys k).snd
ih : x = k' ∨ x ∈ map Prod.fst (groupByKey (matchKey (matchKey ys k).snd k').snd)
⊢ Mem x (map Prod.fst (groupByKey (matchKey (matchKey ys k).snd k').snd)) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_groupByKey_key_or_snd | [1421, 1] | [1468, 25] | cases ih with
| inl => contradiction
| inr => assumption | case inr.inr.a
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxneq : ¬x = k'
this : x ∈ map Prod.fst (matchKey ys k).snd
ih : x = k' ∨ x ∈ map Prod.fst (groupByKey (matchKey (matchKey ys k).snd k').snd)
⊢ Mem x (map Prod.fst (groupByKey (matchKey (matchKey ys k).snd k').snd)) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_groupByKey_key_or_snd | [1421, 1] | [1468, 25] | cases hx with
| head => contradiction
| tail _ htail =>
have := mem_fst_matchKey_key_or_snd htail k
cases this with
| inl => contradiction
| inr => assumption | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxneq : ¬x = k'
⊢ x ∈ map Prod.fst (matchKey ys k).snd | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_groupByKey_key_or_snd | [1421, 1] | [1468, 25] | contradiction | case head
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
k k' : κ
v : ν
ys : List (κ × ν)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
h : ¬(k', v).fst = k
hxneq : ¬(k', v).fst = k'
⊢ (k', v).fst ∈ map Prod.fst (matchKey ys k).snd | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_groupByKey_key_or_snd | [1421, 1] | [1468, 25] | have := mem_fst_matchKey_key_or_snd htail k | case tail
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxneq : ¬x = k'
htail : Mem x (map Prod.fst ys)
⊢ x ∈ map Prod.fst (matchKey ys k).snd | case tail
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxneq : ¬x = k'
htail : Mem x (map Prod.fst ys)
this : x = k ∨ x ∈ map Prod.fst (matchKey ys k).snd
⊢ x ∈ map Prod.fst (matchKey ys k).snd |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_groupByKey_key_or_snd | [1421, 1] | [1468, 25] | cases this with
| inl => contradiction
| inr => assumption | case tail
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxneq : ¬x = k'
htail : Mem x (map Prod.fst ys)
this : x = k ∨ x ∈ map Prod.fst (matchKey ys k).snd
⊢ x ∈ map Prod.fst (matchKey ys k).snd | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_groupByKey_key_or_snd | [1421, 1] | [1468, 25] | contradiction | case tail.inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxneq : ¬x = k'
htail : Mem x (map Prod.fst ys)
h✝ : x = k
⊢ x ∈ map Prod.fst (matchKey ys k).snd | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_groupByKey_key_or_snd | [1421, 1] | [1468, 25] | assumption | case tail.inr
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxneq : ¬x = k'
htail : Mem x (map Prod.fst ys)
h✝ : x ∈ map Prod.fst (matchKey ys k).snd
⊢ x ∈ map Prod.fst (matchKey ys k).snd | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_groupByKey_key_or_snd | [1421, 1] | [1468, 25] | contradiction | case inr.inr.a.inl
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxneq : ¬x = k'
this : x ∈ map Prod.fst (matchKey ys k).snd
h✝ : x = k'
⊢ Mem x (map Prod.fst (groupByKey (matchKey (matchKey ys k).snd k').snd)) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_groupByKey_key_or_snd | [1421, 1] | [1468, 25] | assumption | case inr.inr.a.inr
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
ys✝ : List (κ × ν)
x k : κ
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
hxneq : ¬x = k'
this : x ∈ map Prod.fst (matchKey ys k).snd
h✝ : x ∈ map Prod.fst (groupByKey (matchKey (matchKey ys k).snd k').snd)
⊢ Mem x (map Prod.fst (groupByKey (matchKey (matchKey ys k).snd k').snd)) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fst_groupByKey_key_or_snd | [1421, 1] | [1468, 25] | assumption | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
_x✝ : (ys : List (κ × ν)) ×' (x : κ) ×' (_ : x ∈ map Prod.fst ys) ×' κ
a✝³ :
∀ (y : (ys : List (κ × ν)) ×' (x : κ) ×' (_ : x ∈ map Prod.fst ys) ×' κ),
(invImage
(fun a =>
PSigma.casesOn a fun ys snd => PSigma.casesOn snd fun x snd => PSigma.casesOn snd fun hx snd => length ys)
instWellFoundedRelation).1
y _x✝ →
y.2.1 = y.2.2.2 ∨ y.2.1 ∈ map Prod.fst (groupByKey (matchKey y.1 y.2.2.2).snd)
ys✝ : List (κ × ν)
x✝¹ : (x : κ) ×' (_ : x ∈ map Prod.fst ys✝) ×' κ
a✝² :
∀ (y : (ys : List (κ × ν)) ×' (x : κ) ×' (_ : x ∈ map Prod.fst ys) ×' κ),
(invImage
(fun a =>
PSigma.casesOn a fun ys snd => PSigma.casesOn snd fun x snd => PSigma.casesOn snd fun hx snd => length ys)
instWellFoundedRelation).1
y { fst := ys✝, snd := x✝¹ } →
y.2.1 = y.2.2.2 ∨ y.2.1 ∈ map Prod.fst (groupByKey (matchKey y.1 y.2.2.2).snd)
x : κ
hx✝¹ : (_ : x ∈ map Prod.fst ys✝) ×' κ
a✝¹ :
∀ (y : (ys : List (κ × ν)) ×' (x : κ) ×' (_ : x ∈ map Prod.fst ys) ×' κ),
(invImage
(fun a =>
PSigma.casesOn a fun ys snd => PSigma.casesOn snd fun x snd => PSigma.casesOn snd fun hx snd => length ys)
instWellFoundedRelation).1
y { fst := ys✝, snd := { fst := x, snd := hx✝¹ } } →
y.2.1 = y.2.2.2 ∨ y.2.1 ∈ map Prod.fst (groupByKey (matchKey y.1 y.2.2.2).snd)
hx✝ : x ∈ map Prod.fst ys✝
k : κ
a✝ :
∀ (y : (ys : List (κ × ν)) ×' (x : κ) ×' (_ : x ∈ map Prod.fst ys) ×' κ),
(invImage
(fun a =>
PSigma.casesOn a fun ys snd => PSigma.casesOn snd fun x snd => PSigma.casesOn snd fun hx snd => length ys)
instWellFoundedRelation).1
y { fst := ys✝, snd := { fst := x, snd := { fst := hx✝, snd := k } } } →
y.2.1 = y.2.2.2 ∨ y.2.1 ∈ map Prod.fst (groupByKey (matchKey y.1 y.2.2.2).snd)
h : ¬x = k
k' : κ
v : ν
ys : List (κ × ν)
hx : x ∈ map Prod.fst ((k', v) :: ys)
x✝ :
∀ (y : (ys : List (κ × ν)) ×' (x : κ) ×' (_ : x ∈ map Prod.fst ys) ×' κ),
(invImage
(fun a =>
PSigma.casesOn a fun ys snd => PSigma.casesOn snd fun x snd => PSigma.casesOn snd fun hx snd => length ys)
instWellFoundedRelation).1
y { fst := (k', v) :: ys, snd := { fst := x, snd := { fst := hx, snd := k } } } →
y.2.1 = y.2.2.2 ∨ y.2.1 ∈ map Prod.fst (groupByKey (matchKey y.1 y.2.2.2).snd)
h_term : length (matchKey ys k).snd < Nat.succ (length ys)
h_term' : length ys < Nat.succ (length ys)
hkneq : ¬k' = k
h✝¹ : (_ : k' = k ∨ ¬k' = k) = (_ : k' = k ∨ ¬k' = k)
hxneq : ¬x = k'
h✝ : (_ : x = k' ∨ ¬x = k') = (_ : x = k' ∨ ¬x = k')
this : x ∈ map Prod.fst (matchKey ys k).snd
⊢ (invImage
(fun a =>
PSigma.casesOn a fun ys snd => PSigma.casesOn snd fun x snd => PSigma.casesOn snd fun hx snd => length ys)
instWellFoundedRelation).1
{ fst := (matchKey ys k).snd, snd := { fst := x, snd := { fst := this, snd := k' } } }
{ fst := (k', v) :: ys, snd := { fst := x, snd := { fst := hx, snd := k } } } | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.all_in_map_fst_groupByKey_of_sublist | [1482, 1] | [1515, 25] | simp only [groupByKey] | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
xs✝ ys✝ xs ys : List (κ × ν)
k : κ
v : ν
hsubl : xs <+ ys
x : κ
hx : x ∈ map Prod.fst (groupByKey ((k, v) :: xs))
⊢ x ∈ map Prod.fst (groupByKey ((k, v) :: ys)) | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
xs✝ ys✝ xs ys : List (κ × ν)
k : κ
v : ν
hsubl : xs <+ ys
x : κ
hx : x ∈ map Prod.fst (groupByKey ((k, v) :: xs))
⊢ x ∈ map Prod.fst ((k, v :: (matchKey ys k).fst) :: groupByKey (matchKey ys k).snd) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.all_in_map_fst_groupByKey_of_sublist | [1482, 1] | [1515, 25] | simp only [map] | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
xs✝ ys✝ xs ys : List (κ × ν)
k : κ
v : ν
hsubl : xs <+ ys
x : κ
hx : x ∈ map Prod.fst (groupByKey ((k, v) :: xs))
⊢ x ∈ map Prod.fst ((k, v :: (matchKey ys k).fst) :: groupByKey (matchKey ys k).snd) | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
xs✝ ys✝ xs ys : List (κ × ν)
k : κ
v : ν
hsubl : xs <+ ys
x : κ
hx : x ∈ map Prod.fst (groupByKey ((k, v) :: xs))
⊢ x ∈ k :: map Prod.fst (groupByKey (matchKey ys k).snd) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.all_in_map_fst_groupByKey_of_sublist | [1482, 1] | [1515, 25] | simp only [groupByKey] at hx | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
xs✝ ys✝ xs ys : List (κ × ν)
k : κ
v : ν
hsubl : xs <+ ys
x : κ
hx : x ∈ map Prod.fst (groupByKey ((k, v) :: xs))
⊢ x ∈ k :: map Prod.fst (groupByKey (matchKey ys k).snd) | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
xs✝ ys✝ xs ys : List (κ × ν)
k : κ
v : ν
hsubl : xs <+ ys
x : κ
hx : x ∈ map Prod.fst ((k, v :: (matchKey xs k).fst) :: groupByKey (matchKey xs k).snd)
⊢ x ∈ k :: map Prod.fst (groupByKey (matchKey ys k).snd) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.all_in_map_fst_groupByKey_of_sublist | [1482, 1] | [1515, 25] | simp only [map] at hx | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
xs✝ ys✝ xs ys : List (κ × ν)
k : κ
v : ν
hsubl : xs <+ ys
x : κ
hx : x ∈ map Prod.fst ((k, v :: (matchKey xs k).fst) :: groupByKey (matchKey xs k).snd)
⊢ x ∈ k :: map Prod.fst (groupByKey (matchKey ys k).snd) | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
xs✝ ys✝ xs ys : List (κ × ν)
k : κ
v : ν
hsubl : xs <+ ys
x : κ
hx : x ∈ k :: map Prod.fst (groupByKey (matchKey xs k).snd)
⊢ x ∈ k :: map Prod.fst (groupByKey (matchKey ys k).snd) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.all_in_map_fst_groupByKey_of_sublist | [1482, 1] | [1515, 25] | cases hx with
| head => constructor
| tail _ htail =>
apply Mem.tail
have : (matchKey xs k).snd <+ (matchKey ys k).snd :=
matchKey_snd_sublist_of_sublist _ _ _ hsubl
have hterm := matchKey_length_lt k ys
apply all_in_map_fst_groupByKey_of_sublist this
assumption | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
xs✝ ys✝ xs ys : List (κ × ν)
k : κ
v : ν
hsubl : xs <+ ys
x : κ
hx : x ∈ k :: map Prod.fst (groupByKey (matchKey xs k).snd)
⊢ x ∈ k :: map Prod.fst (groupByKey (matchKey ys k).snd) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.all_in_map_fst_groupByKey_of_sublist | [1482, 1] | [1515, 25] | constructor | case head
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
xs✝ ys✝ xs ys : List (κ × ν)
k : κ
v : ν
hsubl : xs <+ ys
⊢ k ∈ k :: map Prod.fst (groupByKey (matchKey ys k).snd) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.all_in_map_fst_groupByKey_of_sublist | [1482, 1] | [1515, 25] | apply Mem.tail | case tail
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
xs✝ ys✝ xs ys : List (κ × ν)
k : κ
v : ν
hsubl : xs <+ ys
x : κ
htail : Mem x (map Prod.fst (groupByKey (matchKey xs k).snd))
⊢ x ∈ k :: map Prod.fst (groupByKey (matchKey ys k).snd) | case tail.a
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
xs✝ ys✝ xs ys : List (κ × ν)
k : κ
v : ν
hsubl : xs <+ ys
x : κ
htail : Mem x (map Prod.fst (groupByKey (matchKey xs k).snd))
⊢ Mem x (map Prod.fst (groupByKey (matchKey ys k).snd)) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.all_in_map_fst_groupByKey_of_sublist | [1482, 1] | [1515, 25] | have : (matchKey xs k).snd <+ (matchKey ys k).snd :=
matchKey_snd_sublist_of_sublist _ _ _ hsubl | case tail.a
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
xs✝ ys✝ xs ys : List (κ × ν)
k : κ
v : ν
hsubl : xs <+ ys
x : κ
htail : Mem x (map Prod.fst (groupByKey (matchKey xs k).snd))
⊢ Mem x (map Prod.fst (groupByKey (matchKey ys k).snd)) | case tail.a
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
xs✝ ys✝ xs ys : List (κ × ν)
k : κ
v : ν
hsubl : xs <+ ys
x : κ
htail : Mem x (map Prod.fst (groupByKey (matchKey xs k).snd))
this : (matchKey xs k).snd <+ (matchKey ys k).snd
⊢ Mem x (map Prod.fst (groupByKey (matchKey ys k).snd)) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.all_in_map_fst_groupByKey_of_sublist | [1482, 1] | [1515, 25] | have hterm := matchKey_length_lt k ys | case tail.a
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
xs✝ ys✝ xs ys : List (κ × ν)
k : κ
v : ν
hsubl : xs <+ ys
x : κ
htail : Mem x (map Prod.fst (groupByKey (matchKey xs k).snd))
this : (matchKey xs k).snd <+ (matchKey ys k).snd
⊢ Mem x (map Prod.fst (groupByKey (matchKey ys k).snd)) | case tail.a
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
xs✝ ys✝ xs ys : List (κ × ν)
k : κ
v : ν
hsubl : xs <+ ys
x : κ
htail : Mem x (map Prod.fst (groupByKey (matchKey xs k).snd))
this : (matchKey xs k).snd <+ (matchKey ys k).snd
hterm : length (matchKey ys k).snd < Nat.succ (length ys)
⊢ Mem x (map Prod.fst (groupByKey (matchKey ys k).snd)) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.all_in_map_fst_groupByKey_of_sublist | [1482, 1] | [1515, 25] | apply all_in_map_fst_groupByKey_of_sublist this | case tail.a
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
xs✝ ys✝ xs ys : List (κ × ν)
k : κ
v : ν
hsubl : xs <+ ys
x : κ
htail : Mem x (map Prod.fst (groupByKey (matchKey xs k).snd))
this : (matchKey xs k).snd <+ (matchKey ys k).snd
hterm : length (matchKey ys k).snd < Nat.succ (length ys)
⊢ Mem x (map Prod.fst (groupByKey (matchKey ys k).snd)) | case tail.a.a
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
xs✝ ys✝ xs ys : List (κ × ν)
k : κ
v : ν
hsubl : xs <+ ys
x : κ
htail : Mem x (map Prod.fst (groupByKey (matchKey xs k).snd))
this : (matchKey xs k).snd <+ (matchKey ys k).snd
hterm : length (matchKey ys k).snd < Nat.succ (length ys)
⊢ x ∈ map Prod.fst (groupByKey (matchKey xs k).snd) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.all_in_map_fst_groupByKey_of_sublist | [1482, 1] | [1515, 25] | assumption | case tail.a.a
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
xs✝ ys✝ xs ys : List (κ × ν)
k : κ
v : ν
hsubl : xs <+ ys
x : κ
htail : Mem x (map Prod.fst (groupByKey (matchKey xs k).snd))
this : (matchKey xs k).snd <+ (matchKey ys k).snd
hterm : length (matchKey ys k).snd < Nat.succ (length ys)
⊢ x ∈ map Prod.fst (groupByKey (matchKey xs k).snd) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.all_in_map_fst_groupByKey_of_sublist | [1482, 1] | [1515, 25] | assumption | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
_x✝ : (xs : List (κ × ν)) ×' (ys : List (κ × ν)) ×' (_ : xs <+ ys) ×' (x : κ) ×' x ∈ map Prod.fst (groupByKey xs)
a✝⁵ :
∀ (y : (xs : List (κ × ν)) ×' (ys : List (κ × ν)) ×' (_ : xs <+ ys) ×' (x : κ) ×' x ∈ map Prod.fst (groupByKey xs)),
(invImage
(fun a =>
PSigma.casesOn a fun xs snd =>
PSigma.casesOn snd fun ys snd =>
PSigma.casesOn snd fun hsubl snd => PSigma.casesOn snd fun x snd => length ys)
instWellFoundedRelation).1
y _x✝ →
y.2.2.2.1 ∈ map Prod.fst (groupByKey y.2.1)
xs✝ : List (κ × ν)
ys✝¹ : (ys : List (κ × ν)) ×' (_ : xs✝ <+ ys) ×' (x : κ) ×' x ∈ map Prod.fst (groupByKey xs✝)
a✝⁴ :
∀ (y : (xs : List (κ × ν)) ×' (ys : List (κ × ν)) ×' (_ : xs <+ ys) ×' (x : κ) ×' x ∈ map Prod.fst (groupByKey xs)),
(invImage
(fun a =>
PSigma.casesOn a fun xs snd =>
PSigma.casesOn snd fun ys snd =>
PSigma.casesOn snd fun hsubl snd => PSigma.casesOn snd fun x snd => length ys)
instWellFoundedRelation).1
y { fst := xs✝, snd := ys✝¹ } →
y.2.2.2.1 ∈ map Prod.fst (groupByKey y.2.1)
ys✝ : List (κ × ν)
x✝⁶ : (_ : xs✝ <+ ys✝) ×' (x : κ) ×' x ∈ map Prod.fst (groupByKey xs✝)
a✝³ :
∀ (y : (xs : List (κ × ν)) ×' (ys : List (κ × ν)) ×' (_ : xs <+ ys) ×' (x : κ) ×' x ∈ map Prod.fst (groupByKey xs)),
(invImage
(fun a =>
PSigma.casesOn a fun xs snd =>
PSigma.casesOn snd fun ys snd =>
PSigma.casesOn snd fun hsubl snd => PSigma.casesOn snd fun x snd => length ys)
instWellFoundedRelation).1
y { fst := xs✝, snd := { fst := ys✝, snd := x✝⁶ } } →
y.2.2.2.1 ∈ map Prod.fst (groupByKey y.2.1)
x✝⁵ : xs✝ <+ ys✝
x✝⁴ : (x : κ) ×' x ∈ map Prod.fst (groupByKey xs✝)
a✝² :
∀ (y : (xs : List (κ × ν)) ×' (ys : List (κ × ν)) ×' (_ : xs <+ ys) ×' (x : κ) ×' x ∈ map Prod.fst (groupByKey xs)),
(invImage
(fun a =>
PSigma.casesOn a fun xs snd =>
PSigma.casesOn snd fun ys snd =>
PSigma.casesOn snd fun hsubl snd => PSigma.casesOn snd fun x snd => length ys)
instWellFoundedRelation).1
y { fst := xs✝, snd := { fst := ys✝, snd := { fst := x✝⁵, snd := x✝⁴ } } } →
y.2.2.2.1 ∈ map Prod.fst (groupByKey y.2.1)
x✝³ : κ
x✝² : x✝³ ∈ map Prod.fst (groupByKey xs✝)
a✝¹ :
∀ (y : (xs : List (κ × ν)) ×' (ys : List (κ × ν)) ×' (_ : xs <+ ys) ×' (x : κ) ×' x ∈ map Prod.fst (groupByKey xs)),
(invImage
(fun a =>
PSigma.casesOn a fun xs snd =>
PSigma.casesOn snd fun ys snd =>
PSigma.casesOn snd fun hsubl snd => PSigma.casesOn snd fun x snd => length ys)
instWellFoundedRelation).1
y { fst := xs✝, snd := { fst := ys✝, snd := { fst := x✝⁵, snd := { fst := x✝³, snd := x✝² } } } } →
y.2.2.2.1 ∈ map Prod.fst (groupByKey y.2.1)
xs ys : List (κ × ν)
k : κ
v : ν
hsubl : xs <+ ys
x✝¹ : κ
hx : x✝¹ ∈ map Prod.fst (groupByKey ((k, v) :: xs))
x✝ :
∀ (y : (xs : List (κ × ν)) ×' (ys : List (κ × ν)) ×' (_ : xs <+ ys) ×' (x : κ) ×' x ∈ map Prod.fst (groupByKey xs)),
(invImage
(fun a =>
PSigma.casesOn a fun xs snd =>
PSigma.casesOn snd fun ys snd =>
PSigma.casesOn snd fun hsubl snd => PSigma.casesOn snd fun x snd => length ys)
instWellFoundedRelation).1
y
{ fst := (k, v) :: xs,
snd :=
{ fst := (k, v) :: ys,
snd := { fst := (_ : (k, v) :: xs <+ (k, v) :: ys), snd := { fst := x✝¹, snd := hx } } } } →
y.2.2.2.1 ∈ map Prod.fst (groupByKey y.2.1)
b✝ : κ
as✝ : List κ
htail✝ : Mem x✝¹ as✝
h✝¹ : k :: map Prod.fst (groupByKey (matchKey xs k).snd) = b✝ :: as✝
head_eq✝ : k = b✝
tail_eq✝ : map Prod.fst (groupByKey (matchKey xs k).snd) = as✝
htail : Mem x✝¹ (map Prod.fst (groupByKey (matchKey xs k).snd))
h✝ :
HEq
(_ :
x✝¹ ∈
map Prod.fst
(let_fun h_help := (_ : length (matchKey xs k).snd < Nat.succ (length xs));
let fms := matchKey xs k;
(k, v :: fms.fst) :: groupByKey fms.snd))
(_ : Mem x✝¹ (k :: map Prod.fst (groupByKey (matchKey xs k).snd)))
this : (matchKey xs k).snd <+ (matchKey ys k).snd
hterm : length (matchKey ys k).snd < Nat.succ (length ys)
x : κ
a✝ : x ∈ map Prod.fst (groupByKey (matchKey xs k).snd)
⊢ (invImage
(fun a =>
PSigma.casesOn a fun xs snd =>
PSigma.casesOn snd fun ys snd =>
PSigma.casesOn snd fun hsubl snd => PSigma.casesOn snd fun x snd => length ys)
instWellFoundedRelation).1
{ fst := (matchKey xs k).snd,
snd := { fst := (matchKey ys k).snd, snd := { fst := this, snd := { fst := x, snd := a✝ } } } }
{ fst := (k, v) :: xs,
snd :=
{ fst := (k, v) :: ys,
snd := { fst := (_ : (k, v) :: xs <+ (k, v) :: ys), snd := { fst := x✝¹, snd := hx } } } } | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fsts_of_mem_fsts_groupByKey | [1550, 1] | [1566, 17] | intro h | κ : Type u_1
ν : Type u_2
k : κ
inst✝ : DecidableEq κ
kvs : List (κ × ν)
⊢ k ∈ map Prod.fst (groupByKey kvs) → k ∈ map Prod.fst kvs | κ : Type u_1
ν : Type u_2
k : κ
inst✝ : DecidableEq κ
kvs : List (κ × ν)
h : k ∈ map Prod.fst (groupByKey kvs)
⊢ k ∈ map Prod.fst kvs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fsts_of_mem_fsts_groupByKey | [1550, 1] | [1566, 17] | induction kvs with
| nil => contradiction
| cons kv kvs ih =>
cases kv with | mk k₀ v₀ =>
simp only [groupByKey] at h
simp only [map] at h
simp only [map]
cases h with
| head => apply Mem.head
| tail _ htail =>
apply Mem.tail
apply ih
apply all_in_map_fst_groupByKey_of_sublist (matchKey_snd_sublist k₀ kvs)
assumption | κ : Type u_1
ν : Type u_2
k : κ
inst✝ : DecidableEq κ
kvs : List (κ × ν)
h : k ∈ map Prod.fst (groupByKey kvs)
⊢ k ∈ map Prod.fst kvs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fsts_of_mem_fsts_groupByKey | [1550, 1] | [1566, 17] | contradiction | case nil
κ : Type u_1
ν : Type u_2
k : κ
inst✝ : DecidableEq κ
h : k ∈ map Prod.fst (groupByKey [])
⊢ k ∈ map Prod.fst [] | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fsts_of_mem_fsts_groupByKey | [1550, 1] | [1566, 17] | cases kv with | mk k₀ v₀ =>
simp only [groupByKey] at h
simp only [map] at h
simp only [map]
cases h with
| head => apply Mem.head
| tail _ htail =>
apply Mem.tail
apply ih
apply all_in_map_fst_groupByKey_of_sublist (matchKey_snd_sublist k₀ kvs)
assumption | case cons
κ : Type u_1
ν : Type u_2
k : κ
inst✝ : DecidableEq κ
kv : κ × ν
kvs : List (κ × ν)
ih : k ∈ map Prod.fst (groupByKey kvs) → k ∈ map Prod.fst kvs
h : k ∈ map Prod.fst (groupByKey (kv :: kvs))
⊢ k ∈ map Prod.fst (kv :: kvs) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fsts_of_mem_fsts_groupByKey | [1550, 1] | [1566, 17] | simp only [groupByKey] at h | case cons.mk
κ : Type u_1
ν : Type u_2
k : κ
inst✝ : DecidableEq κ
kvs : List (κ × ν)
ih : k ∈ map Prod.fst (groupByKey kvs) → k ∈ map Prod.fst kvs
k₀ : κ
v₀ : ν
h : k ∈ map Prod.fst (groupByKey ((k₀, v₀) :: kvs))
⊢ k ∈ map Prod.fst ((k₀, v₀) :: kvs) | case cons.mk
κ : Type u_1
ν : Type u_2
k : κ
inst✝ : DecidableEq κ
kvs : List (κ × ν)
ih : k ∈ map Prod.fst (groupByKey kvs) → k ∈ map Prod.fst kvs
k₀ : κ
v₀ : ν
h : k ∈ map Prod.fst ((k₀, v₀ :: (matchKey kvs k₀).fst) :: groupByKey (matchKey kvs k₀).snd)
⊢ k ∈ map Prod.fst ((k₀, v₀) :: kvs) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fsts_of_mem_fsts_groupByKey | [1550, 1] | [1566, 17] | simp only [map] at h | case cons.mk
κ : Type u_1
ν : Type u_2
k : κ
inst✝ : DecidableEq κ
kvs : List (κ × ν)
ih : k ∈ map Prod.fst (groupByKey kvs) → k ∈ map Prod.fst kvs
k₀ : κ
v₀ : ν
h : k ∈ map Prod.fst ((k₀, v₀ :: (matchKey kvs k₀).fst) :: groupByKey (matchKey kvs k₀).snd)
⊢ k ∈ map Prod.fst ((k₀, v₀) :: kvs) | case cons.mk
κ : Type u_1
ν : Type u_2
k : κ
inst✝ : DecidableEq κ
kvs : List (κ × ν)
ih : k ∈ map Prod.fst (groupByKey kvs) → k ∈ map Prod.fst kvs
k₀ : κ
v₀ : ν
h : k ∈ k₀ :: map Prod.fst (groupByKey (matchKey kvs k₀).snd)
⊢ k ∈ map Prod.fst ((k₀, v₀) :: kvs) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fsts_of_mem_fsts_groupByKey | [1550, 1] | [1566, 17] | simp only [map] | case cons.mk
κ : Type u_1
ν : Type u_2
k : κ
inst✝ : DecidableEq κ
kvs : List (κ × ν)
ih : k ∈ map Prod.fst (groupByKey kvs) → k ∈ map Prod.fst kvs
k₀ : κ
v₀ : ν
h : k ∈ k₀ :: map Prod.fst (groupByKey (matchKey kvs k₀).snd)
⊢ k ∈ map Prod.fst ((k₀, v₀) :: kvs) | case cons.mk
κ : Type u_1
ν : Type u_2
k : κ
inst✝ : DecidableEq κ
kvs : List (κ × ν)
ih : k ∈ map Prod.fst (groupByKey kvs) → k ∈ map Prod.fst kvs
k₀ : κ
v₀ : ν
h : k ∈ k₀ :: map Prod.fst (groupByKey (matchKey kvs k₀).snd)
⊢ k ∈ k₀ :: map Prod.fst kvs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fsts_of_mem_fsts_groupByKey | [1550, 1] | [1566, 17] | cases h with
| head => apply Mem.head
| tail _ htail =>
apply Mem.tail
apply ih
apply all_in_map_fst_groupByKey_of_sublist (matchKey_snd_sublist k₀ kvs)
assumption | case cons.mk
κ : Type u_1
ν : Type u_2
k : κ
inst✝ : DecidableEq κ
kvs : List (κ × ν)
ih : k ∈ map Prod.fst (groupByKey kvs) → k ∈ map Prod.fst kvs
k₀ : κ
v₀ : ν
h : k ∈ k₀ :: map Prod.fst (groupByKey (matchKey kvs k₀).snd)
⊢ k ∈ k₀ :: map Prod.fst kvs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fsts_of_mem_fsts_groupByKey | [1550, 1] | [1566, 17] | apply Mem.head | case cons.mk.head
κ : Type u_1
ν : Type u_2
k : κ
inst✝ : DecidableEq κ
kvs : List (κ × ν)
ih : k ∈ map Prod.fst (groupByKey kvs) → k ∈ map Prod.fst kvs
v₀ : ν
⊢ k ∈ k :: map Prod.fst kvs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fsts_of_mem_fsts_groupByKey | [1550, 1] | [1566, 17] | apply Mem.tail | case cons.mk.tail
κ : Type u_1
ν : Type u_2
k : κ
inst✝ : DecidableEq κ
kvs : List (κ × ν)
ih : k ∈ map Prod.fst (groupByKey kvs) → k ∈ map Prod.fst kvs
k₀ : κ
v₀ : ν
htail : Mem k (map Prod.fst (groupByKey (matchKey kvs k₀).snd))
⊢ k ∈ k₀ :: map Prod.fst kvs | case cons.mk.tail.a
κ : Type u_1
ν : Type u_2
k : κ
inst✝ : DecidableEq κ
kvs : List (κ × ν)
ih : k ∈ map Prod.fst (groupByKey kvs) → k ∈ map Prod.fst kvs
k₀ : κ
v₀ : ν
htail : Mem k (map Prod.fst (groupByKey (matchKey kvs k₀).snd))
⊢ Mem k (map Prod.fst kvs) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fsts_of_mem_fsts_groupByKey | [1550, 1] | [1566, 17] | apply ih | case cons.mk.tail.a
κ : Type u_1
ν : Type u_2
k : κ
inst✝ : DecidableEq κ
kvs : List (κ × ν)
ih : k ∈ map Prod.fst (groupByKey kvs) → k ∈ map Prod.fst kvs
k₀ : κ
v₀ : ν
htail : Mem k (map Prod.fst (groupByKey (matchKey kvs k₀).snd))
⊢ Mem k (map Prod.fst kvs) | case cons.mk.tail.a
κ : Type u_1
ν : Type u_2
k : κ
inst✝ : DecidableEq κ
kvs : List (κ × ν)
ih : k ∈ map Prod.fst (groupByKey kvs) → k ∈ map Prod.fst kvs
k₀ : κ
v₀ : ν
htail : Mem k (map Prod.fst (groupByKey (matchKey kvs k₀).snd))
⊢ k ∈ map Prod.fst (groupByKey kvs) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fsts_of_mem_fsts_groupByKey | [1550, 1] | [1566, 17] | apply all_in_map_fst_groupByKey_of_sublist (matchKey_snd_sublist k₀ kvs) | case cons.mk.tail.a
κ : Type u_1
ν : Type u_2
k : κ
inst✝ : DecidableEq κ
kvs : List (κ × ν)
ih : k ∈ map Prod.fst (groupByKey kvs) → k ∈ map Prod.fst kvs
k₀ : κ
v₀ : ν
htail : Mem k (map Prod.fst (groupByKey (matchKey kvs k₀).snd))
⊢ k ∈ map Prod.fst (groupByKey kvs) | case cons.mk.tail.a.a
κ : Type u_1
ν : Type u_2
k : κ
inst✝ : DecidableEq κ
kvs : List (κ × ν)
ih : k ∈ map Prod.fst (groupByKey kvs) → k ∈ map Prod.fst kvs
k₀ : κ
v₀ : ν
htail : Mem k (map Prod.fst (groupByKey (matchKey kvs k₀).snd))
⊢ k ∈ map Prod.fst (groupByKey (matchKey kvs k₀).snd) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_fsts_of_mem_fsts_groupByKey | [1550, 1] | [1566, 17] | assumption | case cons.mk.tail.a.a
κ : Type u_1
ν : Type u_2
k : κ
inst✝ : DecidableEq κ
kvs : List (κ × ν)
ih : k ∈ map Prod.fst (groupByKey kvs) → k ∈ map Prod.fst kvs
k₀ : κ
v₀ : ν
htail : Mem k (map Prod.fst (groupByKey (matchKey kvs k₀).snd))
⊢ k ∈ map Prod.fst (groupByKey (matchKey kvs k₀).snd) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.groupByKey_fsts_no_duplicates | [1577, 1] | [1588, 25] | assumption | κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
kvs : List (κ × ν)
a✝ :
∀ (y : List (κ × ν)),
(invImage (fun a => length a) instWellFoundedRelation).1 y kvs → NoDuplicates (map Prod.fst (groupByKey y))
k : κ
v : ν
xs : List (κ × ν)
x✝ :
∀ (y : List (κ × ν)),
(invImage (fun a => length a) instWellFoundedRelation).1 y ((k, v) :: xs) →
NoDuplicates (map Prod.fst (groupByKey y))
h_help : length (matchKey xs k).snd < Nat.succ (length xs)
⊢ (invImage (fun a => length a) instWellFoundedRelation).1 (matchKey xs k).snd ((k, v) :: xs) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_map | [1591, 1] | [1612, 33] | have ih := @mem_map α β f b xs | α : Type u_1
β : Type u_2
f : α → β
b : β
x : α
xs : List α
⊢ b ∈ map f (x :: xs) ↔ ∃ a, a ∈ x :: xs ∧ f a = b | α : Type u_1
β : Type u_2
f : α → β
b : β
x : α
xs : List α
ih : b ∈ map f xs ↔ ∃ a, a ∈ xs ∧ f a = b
⊢ b ∈ map f (x :: xs) ↔ ∃ a, a ∈ x :: xs ∧ f a = b |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_map | [1591, 1] | [1612, 33] | apply Iff.intro | α : Type u_1
β : Type u_2
f : α → β
b : β
x : α
xs : List α
ih : b ∈ map f xs ↔ ∃ a, a ∈ xs ∧ f a = b
⊢ b ∈ map f (x :: xs) ↔ ∃ a, a ∈ x :: xs ∧ f a = b | case mp
α : Type u_1
β : Type u_2
f : α → β
b : β
x : α
xs : List α
ih : b ∈ map f xs ↔ ∃ a, a ∈ xs ∧ f a = b
⊢ b ∈ map f (x :: xs) → ∃ a, a ∈ x :: xs ∧ f a = b
case mpr
α : Type u_1
β : Type u_2
f : α → β
b : β
x : α
xs : List α
ih : b ∈ map f xs ↔ ∃ a, a ∈ xs ∧ f a = b
⊢ (∃ a, a ∈ x :: xs ∧ f a = b) → b ∈ map f (x :: xs) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_map | [1591, 1] | [1612, 33] | . intro h
cases h with
| head =>
exact Exists.intro x (And.intro (List.Mem.head _) rfl)
| tail x h' =>
have ih_val := ih.mp h'
cases ih_val with | intro a ha =>
exact Exists.intro a (And.intro (Mem.tail _ ha.left) ha.right) | case mp
α : Type u_1
β : Type u_2
f : α → β
b : β
x : α
xs : List α
ih : b ∈ map f xs ↔ ∃ a, a ∈ xs ∧ f a = b
⊢ b ∈ map f (x :: xs) → ∃ a, a ∈ x :: xs ∧ f a = b
case mpr
α : Type u_1
β : Type u_2
f : α → β
b : β
x : α
xs : List α
ih : b ∈ map f xs ↔ ∃ a, a ∈ xs ∧ f a = b
⊢ (∃ a, a ∈ x :: xs ∧ f a = b) → b ∈ map f (x :: xs) | case mpr
α : Type u_1
β : Type u_2
f : α → β
b : β
x : α
xs : List α
ih : b ∈ map f xs ↔ ∃ a, a ∈ xs ∧ f a = b
⊢ (∃ a, a ∈ x :: xs ∧ f a = b) → b ∈ map f (x :: xs) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_map | [1591, 1] | [1612, 33] | . intro h
cases h with | intro a ha =>
simp only [map]
cases ha.left with
| head => rw [ha.right]; constructor
| tail x h' =>
have h_in_tail := ih.mpr (Exists.intro a ⟨h', ha.right⟩)
exact Mem.tail _ h_in_tail | case mpr
α : Type u_1
β : Type u_2
f : α → β
b : β
x : α
xs : List α
ih : b ∈ map f xs ↔ ∃ a, a ∈ xs ∧ f a = b
⊢ (∃ a, a ∈ x :: xs ∧ f a = b) → b ∈ map f (x :: xs) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_map | [1591, 1] | [1612, 33] | intro h | case mp
α : Type u_1
β : Type u_2
f : α → β
b : β
x : α
xs : List α
ih : b ∈ map f xs ↔ ∃ a, a ∈ xs ∧ f a = b
⊢ b ∈ map f (x :: xs) → ∃ a, a ∈ x :: xs ∧ f a = b | case mp
α : Type u_1
β : Type u_2
f : α → β
b : β
x : α
xs : List α
ih : b ∈ map f xs ↔ ∃ a, a ∈ xs ∧ f a = b
h : b ∈ map f (x :: xs)
⊢ ∃ a, a ∈ x :: xs ∧ f a = b |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_map | [1591, 1] | [1612, 33] | cases h with
| head =>
exact Exists.intro x (And.intro (List.Mem.head _) rfl)
| tail x h' =>
have ih_val := ih.mp h'
cases ih_val with | intro a ha =>
exact Exists.intro a (And.intro (Mem.tail _ ha.left) ha.right) | case mp
α : Type u_1
β : Type u_2
f : α → β
b : β
x : α
xs : List α
ih : b ∈ map f xs ↔ ∃ a, a ∈ xs ∧ f a = b
h : b ∈ map f (x :: xs)
⊢ ∃ a, a ∈ x :: xs ∧ f a = b | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_map | [1591, 1] | [1612, 33] | exact Exists.intro x (And.intro (List.Mem.head _) rfl) | case mp.head
α : Type u_1
β : Type u_2
f : α → β
x : α
xs : List α
ih : f x ∈ map f xs ↔ ∃ a, a ∈ xs ∧ f a = f x
⊢ ∃ a, a ∈ x :: xs ∧ f a = f x | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_map | [1591, 1] | [1612, 33] | have ih_val := ih.mp h' | case mp.tail
α : Type u_1
β : Type u_2
f : α → β
b : β
x : α
xs : List α
ih : b ∈ map f xs ↔ ∃ a, a ∈ xs ∧ f a = b
h' : Mem b (map f xs)
⊢ ∃ a, a ∈ x :: xs ∧ f a = b | case mp.tail
α : Type u_1
β : Type u_2
f : α → β
b : β
x : α
xs : List α
ih : b ∈ map f xs ↔ ∃ a, a ∈ xs ∧ f a = b
h' : Mem b (map f xs)
ih_val : ∃ a, a ∈ xs ∧ f a = b
⊢ ∃ a, a ∈ x :: xs ∧ f a = b |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_map | [1591, 1] | [1612, 33] | cases ih_val with | intro a ha =>
exact Exists.intro a (And.intro (Mem.tail _ ha.left) ha.right) | case mp.tail
α : Type u_1
β : Type u_2
f : α → β
b : β
x : α
xs : List α
ih : b ∈ map f xs ↔ ∃ a, a ∈ xs ∧ f a = b
h' : Mem b (map f xs)
ih_val : ∃ a, a ∈ xs ∧ f a = b
⊢ ∃ a, a ∈ x :: xs ∧ f a = b | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_map | [1591, 1] | [1612, 33] | exact Exists.intro a (And.intro (Mem.tail _ ha.left) ha.right) | case mp.tail.intro
α : Type u_1
β : Type u_2
f : α → β
b : β
x : α
xs : List α
ih : b ∈ map f xs ↔ ∃ a, a ∈ xs ∧ f a = b
h' : Mem b (map f xs)
a : α
ha : a ∈ xs ∧ f a = b
⊢ ∃ a, a ∈ x :: xs ∧ f a = b | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_map | [1591, 1] | [1612, 33] | intro h | case mpr
α : Type u_1
β : Type u_2
f : α → β
b : β
x : α
xs : List α
ih : b ∈ map f xs ↔ ∃ a, a ∈ xs ∧ f a = b
⊢ (∃ a, a ∈ x :: xs ∧ f a = b) → b ∈ map f (x :: xs) | case mpr
α : Type u_1
β : Type u_2
f : α → β
b : β
x : α
xs : List α
ih : b ∈ map f xs ↔ ∃ a, a ∈ xs ∧ f a = b
h : ∃ a, a ∈ x :: xs ∧ f a = b
⊢ b ∈ map f (x :: xs) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_map | [1591, 1] | [1612, 33] | cases h with | intro a ha =>
simp only [map]
cases ha.left with
| head => rw [ha.right]; constructor
| tail x h' =>
have h_in_tail := ih.mpr (Exists.intro a ⟨h', ha.right⟩)
exact Mem.tail _ h_in_tail | case mpr
α : Type u_1
β : Type u_2
f : α → β
b : β
x : α
xs : List α
ih : b ∈ map f xs ↔ ∃ a, a ∈ xs ∧ f a = b
h : ∃ a, a ∈ x :: xs ∧ f a = b
⊢ b ∈ map f (x :: xs) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_map | [1591, 1] | [1612, 33] | simp only [map] | case mpr.intro
α : Type u_1
β : Type u_2
f : α → β
b : β
x : α
xs : List α
ih : b ∈ map f xs ↔ ∃ a, a ∈ xs ∧ f a = b
a : α
ha : a ∈ x :: xs ∧ f a = b
⊢ b ∈ map f (x :: xs) | case mpr.intro
α : Type u_1
β : Type u_2
f : α → β
b : β
x : α
xs : List α
ih : b ∈ map f xs ↔ ∃ a, a ∈ xs ∧ f a = b
a : α
ha : a ∈ x :: xs ∧ f a = b
⊢ b ∈ f x :: map f xs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_map | [1591, 1] | [1612, 33] | cases ha.left with
| head => rw [ha.right]; constructor
| tail x h' =>
have h_in_tail := ih.mpr (Exists.intro a ⟨h', ha.right⟩)
exact Mem.tail _ h_in_tail | case mpr.intro
α : Type u_1
β : Type u_2
f : α → β
b : β
x : α
xs : List α
ih : b ∈ map f xs ↔ ∃ a, a ∈ xs ∧ f a = b
a : α
ha : a ∈ x :: xs ∧ f a = b
⊢ b ∈ f x :: map f xs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_map | [1591, 1] | [1612, 33] | rw [ha.right] | case mpr.intro.head
α : Type u_1
β : Type u_2
f : α → β
b : β
x : α
xs : List α
ih : b ∈ map f xs ↔ ∃ a, a ∈ xs ∧ f a = b
ha : x ∈ x :: xs ∧ f x = b
⊢ b ∈ f x :: map f xs | case mpr.intro.head
α : Type u_1
β : Type u_2
f : α → β
b : β
x : α
xs : List α
ih : b ∈ map f xs ↔ ∃ a, a ∈ xs ∧ f a = b
ha : x ∈ x :: xs ∧ f x = b
⊢ b ∈ b :: map f xs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_map | [1591, 1] | [1612, 33] | constructor | case mpr.intro.head
α : Type u_1
β : Type u_2
f : α → β
b : β
x : α
xs : List α
ih : b ∈ map f xs ↔ ∃ a, a ∈ xs ∧ f a = b
ha : x ∈ x :: xs ∧ f x = b
⊢ b ∈ b :: map f xs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_map | [1591, 1] | [1612, 33] | have h_in_tail := ih.mpr (Exists.intro a ⟨h', ha.right⟩) | case mpr.intro.tail
α : Type u_1
β : Type u_2
f : α → β
b : β
x : α
xs : List α
ih : b ∈ map f xs ↔ ∃ a, a ∈ xs ∧ f a = b
a : α
ha : a ∈ x :: xs ∧ f a = b
h' : Mem a xs
⊢ b ∈ f x :: map f xs | case mpr.intro.tail
α : Type u_1
β : Type u_2
f : α → β
b : β
x : α
xs : List α
ih : b ∈ map f xs ↔ ∃ a, a ∈ xs ∧ f a = b
a : α
ha : a ∈ x :: xs ∧ f a = b
h' : Mem a xs
h_in_tail : b ∈ map f xs
⊢ b ∈ f x :: map f xs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_map | [1591, 1] | [1612, 33] | exact Mem.tail _ h_in_tail | case mpr.intro.tail
α : Type u_1
β : Type u_2
f : α → β
b : β
x : α
xs : List α
ih : b ∈ map f xs ↔ ∃ a, a ∈ xs ∧ f a = b
a : α
ha : a ∈ x :: xs ∧ f a = b
h' : Mem a xs
h_in_tail : b ∈ map f xs
⊢ b ∈ f x :: map f xs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.map_fst_incrCounts_eq_map_fst | [1651, 1] | [1661, 26] | simp only [map, incrCounts] | α : Type u_1
inst✝ : DecidableEq α
x : α
snd✝ : Nat
as : List (α × Nat)
⊢ map Prod.fst (incrCounts ((x, snd✝) :: as) x) = map Prod.fst ((x, snd✝) :: as) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.map_fst_incrCounts_eq_map_fst | [1651, 1] | [1661, 26] | simp only [map, incrCounts, heq, ite_true, map] | α : Type u_1
inst✝ : DecidableEq α
x : α
a : α × Nat
as : List (α × Nat)
h' : Mem x (map Prod.fst as)
ih : map Prod.fst (incrCounts as x) = map Prod.fst as
heq : a.fst = x
⊢ map Prod.fst (incrCounts (a :: as) x) = map Prod.fst (a :: as) | no goals |
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