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Theorems · Theorem · order theory

Left.mul_pos

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

Assumes left covariance.

Defined in
Mathlib.Algebra.Order.GroupWithZero.Basic
Cited by
2 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
MulZeroClassPreorderPosMulStrictMono
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

mul_pos · cited by 374mul_posdist_integral_mulExpNegMulSq_comp_le · cited by 1dist_integral_mulExpNegMu…Preorder · cited by 7952PreorderMulZeroClass.mul_zero · cited by 2091MulZeroClass.mul_zeroMulZeroClass · cited by 232MulZeroClassPosMulStrictMono · cited by 151PosMulStrictMonomul_lt_mul_of_pos_left · cited by 71mul_lt_mul_of_pos_leftLeft.mul_posCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.