mbk/invariant
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions

list_insert_sorted

Browse source
This commit is contained in:
mehbark 2025-04-03 23:31:28 -04:00
parent cae2737f42
commit 8af59af336
1 changed files with 12 additions and 11 deletions

23
Invariant.lean
View file

@ -50,19 +50,20 @@ theorem list_insert_sorted (hs : List.Sorted (·<·) xs) : List.Sorted (·<·) (
split
· exact List.Sorted.of_cons hs
· split
· rename_i hnlt
exact List.Sorted.cons hnlt hs
· exact List.Sorted.cons ‹_› hs
· have : a < x := by
rename_i hne hnlt
apply Nat.lt_of_le_of_ne
exact Nat.le_of_not_lt hnlt
exact fun a_1 => hne (Eq.symm a_1)
have : a < x := by
rename_i hne hnlt
apply Nat.lt_of_le_of_ne
exact Nat.le_of_not_lt hnlt
exact fun a_1 => hne (Eq.symm a_1)
simp only [List.sorted_cons]
have h : List.Sorted (·<·) as := List.Sorted.of_cons hs
have := ih h
sorry
constructor
· intro b hmem
cases list_insert_mem hmem
<;> simp_all only [imp_self, List.sorted_cons, and_true, not_lt]
· simp_all only [imp_self, List.sorted_cons, and_true, not_lt]
def insert (x : ℕ) : NatSet → NatSet
| ⟨[], _⟩ => singleton x