Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Jump to bottom

[Merged by Bors] - feat(data/nat/fib): add a strict monotonicity lemma. #7317

Closed
wants to merge 1 commit into from
Closed

[Merged by Bors] - feat(data/nat/fib): add a strict monotonicity lemma. #7317

Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
4 changes: 4 additions & 0 deletions src/data/nat/fib.lean
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -82,6 +82,10 @@ lemma fib_le_fib_succ {n : ℕ} : fib n ≤ fib (n + 1) := by { cases n; simp [f
@[mono] lemma fib_mono : monotone fib :=
monotone_of_monotone_nat $ λ _, fib_le_fib_succ

/-- `fib (n + 2)` is strictly monotone. -/
lemma fib_add_two_strict_mono : strict_mono (λ n, fib (n + 2)) :=
strict_mono.nat $ λ n, lt_add_of_pos_left _ $ fib_pos succ_pos'

lemma le_fib_self {n : ℕ} (five_le_n : 5 ≤ n) : n ≤ fib n :=
begin
induction five_le_n with n five_le_n IH,
Expand Down