feat({library,hott}/init/nat): add sub_le_succ

2015-06-15 21:38:41 +10:00 · 2015-06-15 21:38:41 +10:00 · 6b36076ab5
commit 6b36076ab5
parent 3b010b8c92
2 changed files with 2 additions and 0 deletions
--- a/hott/init/nat.hlean
+++ b/hott/init/nat.hlean
@ -287,4 +287,5 @@ namespace nat
    (le.refl a)
    (λ b₁ ih, le.trans !pred_le ih)

+  lemma sub_lt_succ (a b : ℕ) : a - b < succ a := lt_succ_of_le (sub_le a b)
 end nat
--- a/library/init/nat.lean
+++ b/library/init/nat.lean
@ -286,4 +286,5 @@ namespace nat
    (le.refl a)
    (λ b₁ ih, le.trans !pred_le ih)

+  lemma sub_lt_succ (a b : ℕ) : a - b < succ a := lt_succ_of_le (sub_le a b)
 end nat