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Theorems · Theorem · order theory

Right.mul_nonneg

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

Assumes right covariance.

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

Around this declaration

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

Right.neg_of_mul_neg_left · cited by 0Right.neg_of_mul_neg_leftRight.neg_of_mul_neg_right · cited by 0Right.neg_of_mul_neg_rightPreorder · cited by 7952PreorderMulZeroClass.zero_mul · cited by 1625MulZeroClass.zero_mulmul_le_mul_of_nonneg_right · cited by 301mul_le_mul_of_nonneg_rightMulZeroClass · cited by 232MulZeroClassMulPosMono · cited by 128MulPosMonoRight.mul_nonnegCITED 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.