Theorems · Theorem · order theory
Bound.one_lt_mul
∀ {M₀ : Type u_2} [inst : MonoidWithZero M₀] [inst_1 : Preorder M₀] {a b : M₀} [ZeroLEOneClass M₀] [PosMulMono M₀]
[MulPosMono M₀], 1 ≤ a ∧ 1 < b ∨ 1 < a ∧ 1 ≤ b → 1 < a * b- Cited by
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- Foundations
- Depth 9 from the axioms · uses no axioms
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- MonoidWithZerostatement and proof · cited by 456
- ZeroLEOneClassstatement and proof · cited by 304
- PosMulMonostatement and proof · cited by 165
- MulPosMonostatement and proof · cited by 128
- one_lt_mul_of_lt_of_leproof · cited by 3
- one_lt_mulproof · cited by 2
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