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Diffstat (limited to 'Common/Nat.lean')
| -rw-r--r-- | Common/Nat.lean | 6 |
1 files changed, 6 insertions, 0 deletions
diff --git a/Common/Nat.lean b/Common/Nat.lean index fd7337b..5725b6c 100644 --- a/Common/Nat.lean +++ b/Common/Nat.lean @@ -151,3 +151,9 @@ theorem Nat.odd_not_even_odd {n : Nat} : Nat.isOdd n ↔ ¬Nat.isEven n := theorem Nat.even_not_odd_even {n : Nat} : Nat.isEven n ↔ ¬Nat.isOdd n := Iff.intro Nat.even_not_odd Nat.not_odd_even + +theorem Nat.pred_even_odd {n : Nat} (h₁ : Nat.isEven n) (h₂ : n > 0) : Nat.isOdd n.pred := by + cases n with + | zero => contradiction + | succ o => simp[Nat.isEven] at h₁ + assumption |