[Merged by Bors] - feat(SuccPred): {succ,pred}_{min,max} #9367
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pechersky
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Mathlib/Order/SuccPred/Basic.lean
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| theorem succ_max [SuccOrder α] (x y : α) : | ||
| succ (max x y) = max (succ x) (succ y) := by |
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@YaelDillies, is this true as
theorem succ_min [SemilatticeSup α] [SuccOrder α] (x y : α) :
succ (x ⊔ y) = succ x ⊔ succ y := by
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No
Consider, three copies of Nat, two are incomparable and the third one is greater than both. Then a in bottom left copy ⊔ b in bottom right copy = 0 in top copy, so
succ (0 in bottom left copy) ⊔ succ (0 in bottom right copy) = 1 in bottom left copy ⊔ 1 in bottom right copy = 0 in top copysucc (0 in bottom left copy ⊔ 0 in bottom right copy) = succ (0 in top copy) = 1 in top copy.
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