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Theorems · Definition · order theory

FloorSemiring.floor

{α : Type u_4} → {inst : Semiring α} → {inst_1 : PartialOrder α} → [self : FloorSemiring α] → α → ℕ

FloorSemiring.floor a computes the greatest natural n such that (n : α) ≤ a.

Defined in
Mathlib.Algebra.Order.Floor.Defs
Cited by
4 results in Mathlib
Foundations
Depth 2 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.floor · cited by 215Nat.floorFloorSemiring.gc_floor · cited by 3FloorSemiring.gc_floorFloorSemiring.floor_of_neg · cited by 2FloorSemiring.floor_of_negFloorSemiring.natCast_strictMono · cited by 0FloorSemiring.natCast_str…subsingleton_floorSemiring · cited by 0subsingleton_floorSemiringSemiring · cited by 13802SemiringPartialOrder · cited by 6410PartialOrderFloorSemiring · cited by 179FloorSemiringFloorSemiring.floorCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by5

Results whose statement or proof uses this declaration.