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 ∨ ... | 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 = ... | 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 ... | 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' = ... | 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) :: (matchK... |
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) :: (matchK... | 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 ... |
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 => contradi... | 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 ... | 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... | 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 Pro... |
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 Pro... | 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 Pr... | 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 Pro... |
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 Pro... | 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 P... |
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 P... | 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 P... |
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 P... | 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... | 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).... | 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 (matchKe... | 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... |
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... | 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 Pr... | 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 (... | 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 ∈ m... | 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 ∈ m... | 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... | 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 the... |
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 =>
sim... | 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 the... | 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... | 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... |
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... | 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 Pro... |
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 Pro... | 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 ∨ ... |
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 ∨ ... | 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 = ... | 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 ... | 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
(groupByK... | 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... |
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... | 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 :: (mat... |
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 :: (mat... | 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 (... |
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 => contradi... | 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 (... | 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... | 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 Pro... |
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 Pro... | 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 Pr... | 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 Pro... |
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 Pro... | 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 P... |
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 P... | 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 P... |
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 P... | 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... | 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).... | 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 (matchKe... | 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... |
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... | 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 Pr... | 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 (... | 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 ∈ m... | 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 ∈ m... | 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... | 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 (gro... |
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 (gro... | 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 (grou... |
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 (grou... | 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 ... | 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_su... | 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) instWellFoundedRela... | 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 :... |
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 :... | 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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