Theorems · Theorem · order theory
Nat.floor_lt_one
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [inst_2 : FloorSemiring R] {a : R},
0 ≤ a → (⌊a⌋₊ < 1 ↔ a < 1)- Defined in
- Mathlib.Algebra.Order.Floor.Semiring
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- LinearOrderstatement and proof · cited by 8,572
- Nat.cast_oneproof · cited by 2,501
- Nat.floorstatement · cited by 215
- FloorSemiringstatement and proof · cited by 179
- Nat.floor_ltproof · cited by 10
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