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Theorems · Theorem · order theory

Left.mul_lt_mul_of_nonneg

∀ {α : Type u_1} [inst : MulZeroClass α] {a b c d : α} [inst_1 : Preorder α] [PosMulStrictMono α] [MulPosMono α],
  a < b → c < d → 0 ≤ a → 0 ≤ c → a * c < b * d

Assumes left strict covariance.

Defined in
Mathlib.Algebra.Order.GroupWithZero.Basic
Cited by
2 results in Mathlib
Foundations
Depth 8 from the axioms · uses no axioms
Assumes
MulZeroClassPreorderPosMulStrictMonoMulPosMono
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

mul_lt_mul'' · cited by 8mul_lt_mul''mul_lt_mul_of_nonneg · cited by 0mul_lt_mul_of_nonnegPreorder · cited by 7952PreorderLT.lt.le · cited by 2189lt.leLE.le.trans_lt · cited by 795le.trans_ltMulZeroClass · cited by 232MulZeroClassPosMulStrictMono · cited by 151PosMulStrictMonoMulPosMono · cited by 128MulPosMonomul_lt_mul_of_le_of_lt_of_nonneg_of_pos · cited by 5mul_lt_mul_of_le_of_lt_of…Left.mul_lt_mul_of_nonnegCITED BYCITES

Cites7

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Cited by2

Results whose statement or proof uses this declaration.