Theorems · Theorem · order theory
Int.mul_lt_floor
∀ {k : Type u_4} [inst : Field k] [inst_1 : LinearOrder k] [IsOrderedRing k] [inst_3 : FloorRing k] {a b : k},
0 < b → b < 1 → ↑⌈b / (1 - b)⌉ ≤ a → b * a < ↑⌊a⌋- Defined in
- Mathlib.Algebra.Order.Floor.Ring
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Fieldstatement and proof · cited by 7,404
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_zeroproof · cited by 1,870
- IsOrderedRingstatement and proof · cited by 777
- FloorRingstatement and proof · cited by 405
- lt_of_not_geproof · cited by 374
- Int.floorstatement and proof · cited by 225
- Int.ceilstatement and proof · cited by 138
- mul_lt_mul_of_pos_leftproof · cited by 71
- div_le_iff₀'proof · cited by 28
- le_sub_iff_add_le'proof · cited by 23
Cited by1
Results whose statement or proof uses this declaration.
- Int.div_two_lt_floorproof · cited by 0