Mathlib Map

Theorems · Theorem · order theory

strictMonoOn_mul_self

∀ {M₀ : Type u_2} [inst : MonoidWithZero M₀] [inst_1 : PartialOrder M₀] [PosMulStrictMono M₀] [MulPosMono M₀],
  StrictMonoOn (fun x => x * x) {x | 0 ≤ x}
Defined in
Mathlib.Algebra.Order.GroupWithZero.Basic
Cited by
2 results in Mathlib
Foundations
Depth 11 from the axioms · uses no axioms
Assumes
MonoidWithZeroPartialOrderPosMulStrictMonoMulPosMono
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

mul_self_inj · cited by 3mul_self_injmul_self_lt_mul_self_iff · cited by 1mul_self_lt_mul_self_iffPartialOrder · cited by 6410PartialOrderSet.ofPred · cited by 6101Set.ofPredMonoidWithZero · cited by 456MonoidWithZeroStrictMonoOn · cited by 194StrictMonoOnPosMulStrictMono · cited by 151PosMulStrictMonoMulPosMono · cited by 128MulPosMonomul_self_lt_mul_self · cited by 3mul_self_lt_mul_selfstrictMonoOn_mul_selfCITED BYCITES

Cites7

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.