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Theorems · Theorem · order theory

FloorSemiring.gc_floor

∀ {α : Type u_4} {inst : Semiring α} {inst_1 : PartialOrder α} [self : FloorSemiring α] {a : α} {n : ℕ},
  0 ≤ a → (n ≤ FloorSemiring.floor a ↔ ↑n ≤ a)

A natural number n is smaller than FloorSemiring.floor a iff its coercion to α is smaller than a.

Defined in
Mathlib.Algebra.Order.Floor.Defs
Cited by
3 results in Mathlib
Foundations
Depth 12 from the axioms · uses no axioms
Assumes
FloorSemiring
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Around this declaration

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

Nat.le_floor_iff · cited by 24Nat.le_floor_iffFloorSemiring.natCast_strictMono · cited by 0FloorSemiring.natCast_str…subsingleton_floorSemiring · cited by 0subsingleton_floorSemiringSemiring · cited by 13802SemiringPartialOrder · cited by 6410PartialOrderFloorSemiring · cited by 179FloorSemiringFloorSemiring.floor · cited by 4FloorSemiring.floorFloorSemiring.gc_floorCITED BYCITES

Cites4

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Cited by3

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