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.length_counts_aux | [1774, 1] | [1810, 71] | rw [map_fst_incrCounts_eq_cons_fst _ _ hout] | case cons.cons.inr.inr
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih :
∀ (acc : List (α × Nat)),
length (foldl (fun acc v => incrCounts acc v) acc xs) = length (uniqueAux xs (map Prod.fst acc))
a : α × Nat
as : List (α × Nat)
hfalse : ¬a.fst = x
hout : ¬x ∈ map Prod.fst as
this : ¬x ∈ a.fst :: map Prod.... | case cons.cons.inr.inr
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih :
∀ (acc : List (α × Nat)),
length (foldl (fun acc v => incrCounts acc v) acc xs) = length (uniqueAux xs (map Prod.fst acc))
a : α × Nat
as : List (α × Nat)
hfalse : ¬a.fst = x
hout : ¬x ∈ map Prod.fst as
this : ¬x ∈ a.fst :: map Prod.... |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_counts_aux | [1774, 1] | [1810, 71] | apply List.length_uniqueAux_congr_append_cons_acc _ _ _ _ [] | case cons.cons.inr.inr
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih :
∀ (acc : List (α × Nat)),
length (foldl (fun acc v => incrCounts acc v) acc xs) = length (uniqueAux xs (map Prod.fst acc))
a : α × Nat
as : List (α × Nat)
hfalse : ¬a.fst = x
hout : ¬x ∈ map Prod.fst as
this : ¬x ∈ a.fst :: map Prod.... | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_counts_aux | [1774, 1] | [1810, 71] | intros hneg | α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih :
∀ (acc : List (α × Nat)),
length (foldl (fun acc v => incrCounts acc v) acc xs) = length (uniqueAux xs (map Prod.fst acc))
a : α × Nat
as : List (α × Nat)
hfalse : ¬a.fst = x
hout : ¬x ∈ map Prod.fst as
⊢ ¬x ∈ a.fst :: map Prod.fst as | α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih :
∀ (acc : List (α × Nat)),
length (foldl (fun acc v => incrCounts acc v) acc xs) = length (uniqueAux xs (map Prod.fst acc))
a : α × Nat
as : List (α × Nat)
hfalse : ¬a.fst = x
hout : ¬x ∈ map Prod.fst as
hneg : x ∈ a.fst :: map Prod.fst as
⊢ False |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_counts_aux | [1774, 1] | [1810, 71] | cases hneg | α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih :
∀ (acc : List (α × Nat)),
length (foldl (fun acc v => incrCounts acc v) acc xs) = length (uniqueAux xs (map Prod.fst acc))
a : α × Nat
as : List (α × Nat)
hfalse : ¬a.fst = x
hout : ¬x ∈ map Prod.fst as
hneg : x ∈ a.fst :: map Prod.fst as
⊢ False | case head
α : Type u_1
inst✝ : DecidableEq α
xs : List α
ih :
∀ (acc : List (α × Nat)),
length (foldl (fun acc v => incrCounts acc v) acc xs) = length (uniqueAux xs (map Prod.fst acc))
a : α × Nat
as : List (α × Nat)
hfalse : ¬a.fst = a.fst
hout : ¬a.fst ∈ map Prod.fst as
⊢ False
case tail
α : Type u_1
inst✝ : D... |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_counts_aux | [1774, 1] | [1810, 71] | repeat contradiction | case head
α : Type u_1
inst✝ : DecidableEq α
xs : List α
ih :
∀ (acc : List (α × Nat)),
length (foldl (fun acc v => incrCounts acc v) acc xs) = length (uniqueAux xs (map Prod.fst acc))
a : α × Nat
as : List (α × Nat)
hfalse : ¬a.fst = a.fst
hout : ¬a.fst ∈ map Prod.fst as
⊢ False
case tail
α : Type u_1
inst✝ : D... | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_counts_aux | [1774, 1] | [1810, 71] | contradiction | case tail
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih :
∀ (acc : List (α × Nat)),
length (foldl (fun acc v => incrCounts acc v) acc xs) = length (uniqueAux xs (map Prod.fst acc))
a : α × Nat
as : List (α × Nat)
hfalse : ¬a.fst = x
hout : ¬x ∈ map Prod.fst as
a✝ : Mem x (map Prod.fst as)
⊢ False | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_le | [1817, 1] | [1837, 24] | induction xs with
| nil => simp [uniqueAux]
| cons x xs ih =>
intros as
cases Decidable.em (x ∈ as) with
| inl h =>
simp only [length, uniqueAux, h, ite_true]
apply Nat.le_trans
apply ih
rw [Nat.add_assoc, Nat.add_comm 1, ←Nat.add_assoc]
apply Nat.le_step
simp
| inr h =>
simp only [l... | α : Type u_1
inst✝ : DecidableEq α
xs : List α
⊢ ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_le | [1817, 1] | [1837, 24] | simp [uniqueAux] | case nil
α : Type u_1
inst✝ : DecidableEq α
⊢ ∀ (as : List α), length (uniqueAux [] as) ≤ length [] + length as | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_le | [1817, 1] | [1837, 24] | intros as | case cons
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
⊢ ∀ (as : List α), length (uniqueAux (x :: xs) as) ≤ length (x :: xs) + length as | case cons
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
⊢ length (uniqueAux (x :: xs) as) ≤ length (x :: xs) + length as |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_le | [1817, 1] | [1837, 24] | cases Decidable.em (x ∈ as) with
| inl h =>
simp only [length, uniqueAux, h, ite_true]
apply Nat.le_trans
apply ih
rw [Nat.add_assoc, Nat.add_comm 1, ←Nat.add_assoc]
apply Nat.le_step
simp
| inr h =>
simp only [length, uniqueAux, h, ite_false]
apply Nat.le_trans
apply ih
simp only [length]
rw [Nat... | case cons
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
⊢ length (uniqueAux (x :: xs) as) ≤ length (x :: xs) + length as | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_le | [1817, 1] | [1837, 24] | simp only [length, uniqueAux, h, ite_true] | case cons.inl
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : x ∈ as
⊢ length (uniqueAux (x :: xs) as) ≤ length (x :: xs) + length as | case cons.inl
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : x ∈ as
⊢ length (uniqueAux xs as) ≤ length xs + 1 + length as |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_le | [1817, 1] | [1837, 24] | apply Nat.le_trans | case cons.inl
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : x ∈ as
⊢ length (uniqueAux xs as) ≤ length xs + 1 + length as | case cons.inl.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : x ∈ as
⊢ length (uniqueAux xs as) ≤ ?cons.inl.m
case cons.inl.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as)... |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_le | [1817, 1] | [1837, 24] | apply ih | case cons.inl.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : x ∈ as
⊢ length (uniqueAux xs as) ≤ ?cons.inl.m
case cons.inl.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as)... | case cons.inl.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : x ∈ as
⊢ length xs + length as ≤ length xs + 1 + length as |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_le | [1817, 1] | [1837, 24] | rw [Nat.add_assoc, Nat.add_comm 1, ←Nat.add_assoc] | case cons.inl.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : x ∈ as
⊢ length xs + length as ≤ length xs + 1 + length as | case cons.inl.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : x ∈ as
⊢ length xs + length as ≤ length xs + length as + 1 |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_le | [1817, 1] | [1837, 24] | apply Nat.le_step | case cons.inl.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : x ∈ as
⊢ length xs + length as ≤ length xs + length as + 1 | case cons.inl.a.h
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : x ∈ as
⊢ length xs + length as ≤ length xs + length as |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_le | [1817, 1] | [1837, 24] | simp | case cons.inl.a.h
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : x ∈ as
⊢ length xs + length as ≤ length xs + length as | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_le | [1817, 1] | [1837, 24] | simp only [length, uniqueAux, h, ite_false] | case cons.inr
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : ¬x ∈ as
⊢ length (uniqueAux (x :: xs) as) ≤ length (x :: xs) + length as | case cons.inr
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : ¬x ∈ as
⊢ length (uniqueAux xs (x :: as)) ≤ length xs + 1 + length as |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_le | [1817, 1] | [1837, 24] | apply Nat.le_trans | case cons.inr
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : ¬x ∈ as
⊢ length (uniqueAux xs (x :: as)) ≤ length xs + 1 + length as | case cons.inr.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : ¬x ∈ as
⊢ length (uniqueAux xs (x :: as)) ≤ ?cons.inr.m
case cons.inr.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAu... |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_le | [1817, 1] | [1837, 24] | apply ih | case cons.inr.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : ¬x ∈ as
⊢ length (uniqueAux xs (x :: as)) ≤ ?cons.inr.m
case cons.inr.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAu... | case cons.inr.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : ¬x ∈ as
⊢ length xs + length (x :: as) ≤ length xs + 1 + length as |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_le | [1817, 1] | [1837, 24] | simp only [length] | case cons.inr.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : ¬x ∈ as
⊢ length xs + length (x :: as) ≤ length xs + 1 + length as | case cons.inr.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : ¬x ∈ as
⊢ length xs + (length as + 1) ≤ length xs + 1 + length as |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_le | [1817, 1] | [1837, 24] | rw [Nat.add_comm _ 1, Nat.add_assoc] | case cons.inr.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : ¬x ∈ as
⊢ length xs + (length as + 1) ≤ length xs + 1 + length as | case cons.inr.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : ¬x ∈ as
⊢ length xs + (1 + length as) ≤ length xs + (1 + length as) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_le | [1817, 1] | [1837, 24] | apply Nat.le_refl | case cons.inr.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : ¬x ∈ as
⊢ length xs + (1 + length as) ≤ length xs + (1 + length as) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | simp only [get, sieve] at * | α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get (x :: xs) { val := Nat.succ n, isLt := pf1 } ∈ sieve (true :: bs) (x :: xs)
⊢ get (true :: bs) { val := Nat.succ n, isLt := pf2 } = true | α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | apply Iff.mp | α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true | case self
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ ?a ↔ get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = ... |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | apply sieve_mem_iff_true_unique | case self
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ ?a ↔ get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = ... | case self.pf1
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ n < length ?self.xs
case self.hu
α : Type u_1
n : Nat
x : α
... |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | . apply Nat.lt_of_succ_lt_succ pf1 | case self.pf1
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ n < length ?self.xs
case self.hu
α : Type u_1
n : Nat
x : α
... | case self.hu
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ Unique xs
case a
α : Type u_1
n : Nat
x : α
xs : List α
bs : ... |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | . exact hu' | case self.hu
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ Unique xs
case a
α : Type u_1
n : Nat
x : α
xs : List α
bs : ... | case a
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ get xs { val := n, isLt := (_ : n < length xs) } ∈ sieve bs xs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | . exact List.get_mem_cons_of_head_not_mem_getee hf hnmem | case a
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ get xs { val := n, isLt := (_ : n < length xs) } ∈ sieve bs xs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | apply Nat.lt_of_succ_lt_succ pf1 | case self.pf1
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ n < length ?self.xs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | exact hu' | case self.hu
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ Unique xs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | exact List.get_mem_cons_of_head_not_mem_getee hf hnmem | case a
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ get xs { val := n, isLt := (_ : n < length xs) } ∈ sieve bs xs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | simp only [get, sieve] at * | α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get (true :: bs) { val := Nat.succ n, isLt := pf2 } = true
⊢ get (x :: xs) { val := Nat.succ n, isLt := pf1 } ∈ sieve (true :: bs) (x :: xs) | α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | apply Mem.tail | α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs | case a
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ Mem (get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) }) (sieve bs xs) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | apply Iff.mpr | case a
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ Mem (get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) }) (sieve bs xs) | case a.self
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ Mem (get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) }) (sieve bs x... |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | apply sieve_mem_iff_true_unique | case a.self
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ Mem (get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) }) (sieve bs x... | case a.self.pf2
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ n < length bs
case a.self.hu
α : Type u_1
n : Nat
x : α
xs : List α
bs... |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | . apply Nat.lt_of_succ_lt_succ pf2 | case a.self.pf2
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ n < length bs
case a.self.hu
α : Type u_1
n : Nat
x : α
xs : List α
bs... | case a.self.hu
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ Unique xs
case a.a
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Boo... |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | . exact hu' | case a.self.hu
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ Unique xs
case a.a
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Boo... | case a.a
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ get bs { val := n, isLt := (_ : n < length bs) } = true |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | . exact hb | case a.a
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ get bs { val := n, isLt := (_ : n < length bs) } = true | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | apply Nat.lt_of_succ_lt_succ pf2 | case a.self.pf2
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ n < length bs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | exact hu' | case a.self.hu
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ Unique xs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | exact hb | case a.a
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ get bs { val := n, isLt := (_ : n < length bs) } = true | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | intro i xs bs pf1 pf2 f hu | α : Type u_1
β : Type u_2
⊢ ∀ {i : Nat} {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs) (f : α → β),
Unique (map f xs) →
(get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) ↔
get bs { val := i, isLt := pf2 } = true) | α : Type u_1
β : Type u_2
i : Nat
xs : List α
bs : List Bool
pf1 : i < length xs
pf2 : i < length bs
f : α → β
hu : Unique (map f xs)
⊢ get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) ↔
get bs { val := i, isLt := pf2 } = true |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | apply Iff.intro | α : Type u_1
β : Type u_2
i : Nat
xs : List α
bs : List Bool
pf1 : i < length xs
pf2 : i < length bs
f : α → β
hu : Unique (map f xs)
⊢ get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) ↔
get bs { val := i, isLt := pf2 } = true | case mp
α : Type u_1
β : Type u_2
i : Nat
xs : List α
bs : List Bool
pf1 : i < length xs
pf2 : i < length bs
f : α → β
hu : Unique (map f xs)
⊢ get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
case mpr
α : Type u_1
β : Type u_2
i : Nat... |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | . intro hf
induction i generalizing xs bs with
| zero =>
match bs, xs, hu with
| b :: bs, x :: xs, .cons hnmem hu =>
cases b with
| true => simp only [get, sieve] at *
| false =>
simp only [get, sieve] at *
exact mt mem_map_sieve_of_mem_map hnmem hf
| succ i ih =>
match bs, xs,... | case mp
α : Type u_1
β : Type u_2
i : Nat
xs : List α
bs : List Bool
pf1 : i < length xs
pf2 : i < length bs
f : α → β
hu : Unique (map f xs)
⊢ get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
case mpr
α : Type u_1
β : Type u_2
i : Nat... | case mpr
α : Type u_1
β : Type u_2
i : Nat
xs : List α
bs : List Bool
pf1 : i < length xs
pf2 : i < length bs
f : α → β
hu : Unique (map f xs)
⊢ get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | . intro hget
induction i generalizing xs bs with
| zero =>
match bs, xs with
| b :: bs, x :: xs =>
cases b with
| true => exact Mem.head _
| false => simp only [get, map] at hget
| succ i ih =>
match bs, xs, hu with
| b :: bs, x :: xs, .cons hnmem hu =>
cases b with
| true =>
... | case mpr
α : Type u_1
β : Type u_2
i : Nat
xs : List α
bs : List Bool
pf1 : i < length xs
pf2 : i < length bs
f : α → β
hu : Unique (map f xs)
⊢ get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | intro hf | case mp
α : Type u_1
β : Type u_2
i : Nat
xs : List α
bs : List Bool
pf1 : i < length xs
pf2 : i < length bs
f : α → β
hu : Unique (map f xs)
⊢ get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true | case mp
α : Type u_1
β : Type u_2
i : Nat
xs : List α
bs : List Bool
pf1 : i < length xs
pf2 : i < length bs
f : α → β
hu : Unique (map f xs)
hf : get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
⊢ get bs { val := i, isLt := pf2 } = true |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | induction i generalizing xs bs with
| zero =>
match bs, xs, hu with
| b :: bs, x :: xs, .cons hnmem hu =>
cases b with
| true => simp only [get, sieve] at *
| false =>
simp only [get, sieve] at *
exact mt mem_map_sieve_of_mem_map hnmem hf
| succ i ih =>
match bs, xs, hu with
| b :: bs, x :: xs, .c... | case mp
α : Type u_1
β : Type u_2
i : Nat
xs : List α
bs : List Bool
pf1 : i < length xs
pf2 : i < length bs
f : α → β
hu : Unique (map f xs)
hf : get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
⊢ get bs { val := i, isLt := pf2 } = true | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | match bs, xs, hu with
| b :: bs, x :: xs, .cons hnmem hu =>
cases b with
| true => simp only [get, sieve] at *
| false =>
simp only [get, sieve] at *
exact mt mem_map_sieve_of_mem_map hnmem hf | case mp.zero
α : Type u_1
β : Type u_2
f : α → β
xs : List α
bs : List Bool
pf1 : Nat.zero < length xs
pf2 : Nat.zero < length bs
hu : Unique (map f xs)
hf : get (map f xs) { val := Nat.zero, isLt := (_ : Nat.zero < length (map f xs)) } ∈ map f (sieve bs xs)
⊢ get bs { val := Nat.zero, isLt := pf2 } = true | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | cases b with
| true => simp only [get, sieve] at *
| false =>
simp only [get, sieve] at *
exact mt mem_map_sieve_of_mem_map hnmem hf | α : Type u_1
β : Type u_2
f : α → β
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
b : Bool
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.zero < length (x :: xs)
pf2 : Nat.zero < length (b :: bs)
hf :
get (map f (x :: xs)) { val := Nat.zero, isLt := (_ : Nat.zero < l... | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | simp only [get, sieve] at * | case true
α : Type u_1
β : Type u_2
f : α → β
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.zero < length (x :: xs)
pf2 : Nat.zero < length (true :: bs)
hf :
get (map f (x :: xs)) { val := Nat.zero, isLt := (_ : Nat.zero... | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | simp only [get, sieve] at * | case false
α : Type u_1
β : Type u_2
f : α → β
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.zero < length (x :: xs)
pf2 : Nat.zero < length (false :: bs)
hf :
get (map f (x :: xs)) { val := Nat.zero, isLt := (_ : Nat.ze... | case false
α : Type u_1
β : Type u_2
f : α → β
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.zero < length (x :: xs)
pf2 : Nat.zero < length (false :: bs)
hf : f x ∈ map f (sieve bs xs)
⊢ False |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | exact mt mem_map_sieve_of_mem_map hnmem hf | case false
α : Type u_1
β : Type u_2
f : α → β
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.zero < length (x :: xs)
pf2 : Nat.zero < length (false :: bs)
hf : f x ∈ map f (sieve bs xs)
⊢ False | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | match bs, xs, hu with
| b :: bs, x :: xs, .cons hnmem hu =>
cases b with
| true =>
simp only [get, sieve, map] at *
apply ih
. exact hu
. apply get_mem_cons_of_head_not_mem_getee hf hnmem
. apply Nat.lt_of_succ_lt_succ pf1
| false =>
simp only [get, sieve, map] at *
apply ih
. exact hu
. exact hf
. ... | case mp.succ
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs : List α... | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | cases b with
| true =>
simp only [get, sieve, map] at *
apply ih
. exact hu
. apply get_mem_cons_of_head_not_mem_getee hf hnmem
. apply Nat.lt_of_succ_lt_succ pf1
| false =>
simp only [get, sieve, map] at *
apply ih
. exact hu
. exact hf
. apply Nat.lt_of_succ_lt_succ pf1 | α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List ... | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | simp only [get, sieve, map] at * | case true
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
b... | case true
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
b... |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | apply ih | case true
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
b... | case true.hu
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List ... |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | . exact hu | case true.hu
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List ... | case true.hf
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List ... |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | . apply get_mem_cons_of_head_not_mem_getee hf hnmem | case true.hf
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List ... | case true.pf1
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List... |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | . apply Nat.lt_of_succ_lt_succ pf1 | case true.pf1
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List... | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | exact hu | case true.hu
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List ... | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | apply get_mem_cons_of_head_not_mem_getee hf hnmem | case true.hf
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List ... | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | apply Nat.lt_of_succ_lt_succ pf1 | case true.pf1
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List... | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | simp only [get, sieve, map] at * | case false
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
... | case false
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
... |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | apply ih | case false
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
... | case false.hu
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List... |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | . exact hu | case false.hu
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List... | case false.hf
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List... |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | . exact hf | case false.hf
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List... | case false.pf1
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : Lis... |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | . apply Nat.lt_of_succ_lt_succ pf1 | case false.pf1
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : Lis... | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | exact hu | case false.hu
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List... | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | exact hf | case false.hf
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List... | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | apply Nat.lt_of_succ_lt_succ pf1 | case false.pf1
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : Lis... | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | intro hget | case mpr
α : Type u_1
β : Type u_2
i : Nat
xs : List α
bs : List Bool
pf1 : i < length xs
pf2 : i < length bs
f : α → β
hu : Unique (map f xs)
⊢ get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) | case mpr
α : Type u_1
β : Type u_2
i : Nat
xs : List α
bs : List Bool
pf1 : i < length xs
pf2 : i < length bs
f : α → β
hu : Unique (map f xs)
hget : get bs { val := i, isLt := pf2 } = true
⊢ get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | induction i generalizing xs bs with
| zero =>
match bs, xs with
| b :: bs, x :: xs =>
cases b with
| true => exact Mem.head _
| false => simp only [get, map] at hget
| succ i ih =>
match bs, xs, hu with
| b :: bs, x :: xs, .cons hnmem hu =>
cases b with
| true =>
simp only [get, sieve, map] at *
... | case mpr
α : Type u_1
β : Type u_2
i : Nat
xs : List α
bs : List Bool
pf1 : i < length xs
pf2 : i < length bs
f : α → β
hu : Unique (map f xs)
hget : get bs { val := i, isLt := pf2 } = true
⊢ get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | match bs, xs with
| b :: bs, x :: xs =>
cases b with
| true => exact Mem.head _
| false => simp only [get, map] at hget | case mpr.zero
α : Type u_1
β : Type u_2
f : α → β
xs : List α
bs : List Bool
pf1 : Nat.zero < length xs
pf2 : Nat.zero < length bs
hu : Unique (map f xs)
hget : get bs { val := Nat.zero, isLt := pf2 } = true
⊢ get (map f xs) { val := Nat.zero, isLt := (_ : Nat.zero < length (map f xs)) } ∈ map f (sieve bs xs) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | cases b with
| true => exact Mem.head _
| false => simp only [get, map] at hget | α : Type u_1
β : Type u_2
f : α → β
xs✝ : List α
bs✝ : List Bool
b : Bool
bs : List Bool
x : α
xs : List α
pf1 : Nat.zero < length (x :: xs)
pf2 : Nat.zero < length (b :: bs)
hu : Unique (map f (x :: xs))
hget : get (b :: bs) { val := Nat.zero, isLt := pf2 } = true
⊢ get (map f (x :: xs)) { val := Nat.zero, isLt := (_ ... | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | exact Mem.head _ | case true
α : Type u_1
β : Type u_2
f : α → β
xs✝ : List α
bs✝ bs : List Bool
x : α
xs : List α
pf1 : Nat.zero < length (x :: xs)
hu : Unique (map f (x :: xs))
pf2 : Nat.zero < length (true :: bs)
hget : get (true :: bs) { val := Nat.zero, isLt := pf2 } = true
⊢ get (map f (x :: xs)) { val := Nat.zero, isLt := (_ : Nat... | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | simp only [get, map] at hget | case false
α : Type u_1
β : Type u_2
f : α → β
xs✝ : List α
bs✝ bs : List Bool
x : α
xs : List α
pf1 : Nat.zero < length (x :: xs)
hu : Unique (map f (x :: xs))
pf2 : Nat.zero < length (false :: bs)
hget : get (false :: bs) { val := Nat.zero, isLt := pf2 } = true
⊢ get (map f (x :: xs)) { val := Nat.zero, isLt := (_ : ... | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | match bs, xs, hu with
| b :: bs, x :: xs, .cons hnmem hu =>
cases b with
| true =>
simp only [get, sieve, map] at *
apply Mem.tail
apply ih
. apply Nat.lt_of_succ_lt_succ pf1
. exact hu
. exact hget
| false =>
simp only [get, map, sieve] at *
apply ih
. apply Nat.lt_of_succ_lt_succ pf1
. exact hu
... | case mpr.succ
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs : List ... | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | cases b with
| true =>
simp only [get, sieve, map] at *
apply Mem.tail
apply ih
. apply Nat.lt_of_succ_lt_succ pf1
. exact hu
. exact hget
| false =>
simp only [get, map, sieve] at *
apply ih
. apply Nat.lt_of_succ_lt_succ pf1
. exact hu
. exact hget | α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List ... | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | simp only [get, sieve, map] at * | case true
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
b... | case true
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
b... |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | apply Mem.tail | case true
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
b... | case true.a
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α... |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | apply ih | case true.a
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α... | case true.a.pf1
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : Li... |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | . apply Nat.lt_of_succ_lt_succ pf1 | case true.a.pf1
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : Li... | case true.a.hu
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : Lis... |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | . exact hu | case true.a.hu
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : Lis... | case true.a.hget
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : L... |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | . exact hget | case true.a.hget
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : L... | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | apply Nat.lt_of_succ_lt_succ pf1 | case true.a.pf1
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : Li... | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | exact hu | case true.a.hu
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : Lis... | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | exact hget | case true.a.hget
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : L... | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | simp only [get, map, sieve] at * | case false
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
... | case false
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
... |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | apply ih | case false
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
... | case false.pf1
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : Lis... |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | . apply Nat.lt_of_succ_lt_succ pf1 | case false.pf1
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : Lis... | case false.hu
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List... |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | . exact hu | case false.hu
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List... | case false.hget
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : Li... |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | . exact hget | case false.hget
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : Li... | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | apply Nat.lt_of_succ_lt_succ pf1 | case false.pf1
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : Lis... | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | exact hu | case false.hu
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List... | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | exact hget | case false.hget
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : Li... | no goals |
https://github.com/b-mehta/ExponentialRamsey.git | 7e17b629a915a082869f494c8afa56a3e1c7a88d | ExponentialRamsey/Prereq/Mathlib/Analysis/Calculus/Taylor.lean | uIoo_of_le | [29, 1] | [30, 47] | rw [uIoo, inf_eq_left.2 h, sup_eq_right.2 h] | α : Type u_1
inst✝ : Lattice α
x y : α
h : x ≤ y
⊢ uIoo x y = Ioo x y | no goals |
https://github.com/b-mehta/ExponentialRamsey.git | 7e17b629a915a082869f494c8afa56a3e1c7a88d | ExponentialRamsey/Prereq/Mathlib/Analysis/Calculus/Taylor.lean | uIoo_of_ge | [32, 1] | [33, 47] | rw [uIoo, inf_eq_right.2 h, sup_eq_left.2 h] | α : Type u_1
inst✝ : Lattice α
x y : α
h : y ≤ x
⊢ uIoo x y = Ioo y x | no goals |
https://github.com/b-mehta/ExponentialRamsey.git | 7e17b629a915a082869f494c8afa56a3e1c7a88d | ExponentialRamsey/Prereq/Mathlib/Analysis/Calculus/Taylor.lean | uIoo_comm | [35, 1] | [35, 92] | rw [uIoo, uIoo, inf_comm, sup_comm] | α : Type u_1
inst✝ : Lattice α
x y : α
⊢ uIoo x y = uIoo y x | no goals |
https://github.com/b-mehta/ExponentialRamsey.git | 7e17b629a915a082869f494c8afa56a3e1c7a88d | ExponentialRamsey/Prereq/Mathlib/Analysis/Calculus/Taylor.lean | taylor_mean_remainder_unordered | [43, 1] | [71, 7] | rcases Ne.lt_or_lt hx with (hx₀ | hx₀) | f g g' : ℝ → ℝ
x x₀ : ℝ
n : ℕ
hx : x₀ ≠ x
hf : ContDiffOn ℝ (↑n) f (uIcc x₀ x)
hf' : DifferentiableOn ℝ (iteratedDerivWithin n f (uIcc x₀ x)) (uIoo x₀ x)
gcont : ContinuousOn g (uIcc x₀ x)
gdiff : ∀ x_1 ∈ uIoo x₀ x, HasDerivAt g (g' x_1) x_1
g'_ne : ∀ x_1 ∈ uIoo x₀ x, g' x_1 ≠ 0
⊢ ∃ x',
∃ (_ : x' ∈ uIoo x₀ x),
... | case inl
f g g' : ℝ → ℝ
x x₀ : ℝ
n : ℕ
hx : x₀ ≠ x
hf : ContDiffOn ℝ (↑n) f (uIcc x₀ x)
hf' : DifferentiableOn ℝ (iteratedDerivWithin n f (uIcc x₀ x)) (uIoo x₀ x)
gcont : ContinuousOn g (uIcc x₀ x)
gdiff : ∀ x_1 ∈ uIoo x₀ x, HasDerivAt g (g' x_1) x_1
g'_ne : ∀ x_1 ∈ uIoo x₀ x, g' x_1 ≠ 0
hx₀ : x₀ < x
⊢ ∃ x',
∃ (_ :... |
https://github.com/b-mehta/ExponentialRamsey.git | 7e17b629a915a082869f494c8afa56a3e1c7a88d | ExponentialRamsey/Prereq/Mathlib/Analysis/Calculus/Taylor.lean | taylor_mean_remainder_unordered | [43, 1] | [71, 7] | rw [uIcc_of_ge hx₀.le] at hf hf' gcont ⊢ | case inr
f g g' : ℝ → ℝ
x x₀ : ℝ
n : ℕ
hx : x₀ ≠ x
hf : ContDiffOn ℝ (↑n) f (uIcc x₀ x)
hf' : DifferentiableOn ℝ (iteratedDerivWithin n f (uIcc x₀ x)) (uIoo x₀ x)
gcont : ContinuousOn g (uIcc x₀ x)
gdiff : ∀ x_1 ∈ uIoo x₀ x, HasDerivAt g (g' x_1) x_1
g'_ne : ∀ x_1 ∈ uIoo x₀ x, g' x_1 ≠ 0
hx₀ : x < x₀
⊢ ∃ x',
∃ (_ :... | case inr
f g g' : ℝ → ℝ
x x₀ : ℝ
n : ℕ
hx : x₀ ≠ x
hf : ContDiffOn ℝ (↑n) f (Icc x x₀)
hf' : DifferentiableOn ℝ (iteratedDerivWithin n f (Icc x x₀)) (uIoo x₀ x)
gcont : ContinuousOn g (Icc x x₀)
gdiff : ∀ x_1 ∈ uIoo x₀ x, HasDerivAt g (g' x_1) x_1
g'_ne : ∀ x_1 ∈ uIoo x₀ x, g' x_1 ≠ 0
hx₀ : x < x₀
⊢ ∃ x',
∃ (_ : x'... |
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