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Theorems · Theorem · order theory

strictMono_mul_left_of_pos

∀ {M₀ : Type u_2} [inst : MonoidWithZero M₀] [inst_1 : PartialOrder M₀] {a : M₀} [PosMulStrictMono M₀],
  0 < a → StrictMono fun x => a * x
Defined in
Mathlib.Algebra.Order.GroupWithZero.Basic
Cited by
3 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
MonoidWithZeroPartialOrderPosMulStrictMono
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Around this declaration

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

StrictMono.const_mul · cited by 2StrictMono.const_mulStrictAnti.const_mul · cited by 1StrictAnti.const_mulcmp_mul_pos_left · cited by 1cmp_mul_pos_leftPartialOrder · cited by 6410PartialOrderStrictMono · cited by 706StrictMonoMonoidWithZero · cited by 456MonoidWithZeroPosMulStrictMono · cited by 151PosMulStrictMonomul_lt_mul_of_pos_left · cited by 71mul_lt_mul_of_pos_leftstrictMono_mul_left_of_posCITED BYCITES

Cites5

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Cited by3

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