Theorems · Theorem · order theory
Nat.ceil_le_two_mul
∀ {K : Type u_2} [inst : Field K] [inst_1 : LinearOrder K] [IsOrderedRing K] [inst_3 : FloorSemiring K] {a : K},
2⁻¹ ≤ a → ↑⌈a⌉₊ ≤ 2 * a- Defined in
- Mathlib.Algebra.Order.Floor.Semifield
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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
- IsOrderedRingstatement and proof · cited by 777
- one_divproof · cited by 624
- FloorSemiringstatement and proof · cited by 179
- Nat.ceilstatement and proof · cited by 141
- one_lt_twoproof · cited by 67
- Nat.ceil_oneproof · cited by 6
- Nat.ceil_le_mulproof · cited by 1
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