Theorems · Theorem · order theory
one_lt_mul_of_lt_of_le
∀ {M₀ : Type u_2} [inst : MonoidWithZero M₀] [inst_1 : Preorder M₀] {a b : M₀} [ZeroLEOneClass M₀] [PosMulMono M₀],
1 < a → 1 ≤ b → 1 < a * b- Cited by
- 3 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- LE.le.transproof · cited by 3,151
- LT.lt.leproof · cited by 2,189
- LT.lt.trans_leproof · cited by 678
- MonoidWithZerostatement and proof · cited by 456
- zero_le_oneproof · cited by 316
- ZeroLEOneClassstatement and proof · cited by 304
- PosMulMonostatement and proof · cited by 165
- le_mul_of_one_le_rightproof · cited by 15
Cited by3
Results whose statement or proof uses this declaration.
- one_lt_pow₀proof · cited by 18
- IsPrimitiveRoot.not_exists_int_prime_dvd_sub_of_prime_pow_ne_twoproof · cited by 1
- Bound.one_lt_mulproof · cited by 0