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Theorems · Theorem · order theory

mul_left_mono

∀ {α : Type u_1} [inst : Mul α] [inst_1 : Preorder α] [MulRightMono α] {a : α}, Monotone fun x => x * a
Defined in
Mathlib.Algebra.Order.Monoid.Unbundled.Basic
Cited by
10 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
MulPreorderMulRightMono
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

ENNReal.sub_mul · cited by 8ENNReal.sub_mulLipschitzWith.weaken · cited by 4LipschitzWith.weakenmax_mul · cited by 3max_mulMonotone.mul_const' · cited by 2Monotone.mul_const'LipschitzOnWith.weaken · cited by 1LipschitzOnWith.weakenAntitone.mul_const' · cited by 0Antitone.mul_const'min_mul · cited by 0min_mulMonotoneOn.mul_const' · cited by 0MonotoneOn.mul_const'one_add_kstar_mul · cited by 0one_add_kstar_mulAntitoneOn.mul_const' · cited by 0AntitoneOn.mul_const'Preorder · cited by 7952PreorderMonotone · cited by 1397MonotoneMulRightMono · cited by 263MulRightMonomul_le_mul_left · cited by 31mul_le_mul_leftmul_left_monoCITED BYCITES

Cites4

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

Cited by10

Results whose statement or proof uses this declaration.