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Theorems · Theorem · logic and foundations

Nat.Subtype.le_succ_of_forall_lt_le

∀ {s : Set ℕ} [inst : Infinite ↑s] [inst_1 : DecidablePred fun x => x ∈ s] {x y : ↑s},
  (∀ z < x, z ≤ y) → x ≤ Nat.Subtype.succ y
Defined in
Mathlib.Logic.Denumerable
Cited by
1 results in Mathlib
Foundations
Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
InfiniteDecidablePred
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Nat.Subtype.ofNat_surjective · cited by 1Subtype.ofNat_surjectiveSet · cited by 53352SetSet.Elem · cited by 7166Set.Elemle_of_not_gt · cited by 430le_of_not_gtInfinite · cited by 352InfiniteLE.le.not_gt · cited by 189le.not_gtNat.find · cited by 139Nat.findNat.find_spec · cited by 74Nat.find_specNat.Subtype.succ · cited by 6Subtype.succNat.Subtype.exists_succ · cited by 3Subtype.exists_succSubtype.le_succ_of_forall_lt_…CITED BYCITES

Cites9

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Cited by1

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