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Theorems · Theorem · order theory

strictMono_mul_right_of_pos

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

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

StrictMono.mul_const · cited by 2StrictMono.mul_constStrictAnti.mul_const · cited by 0StrictAnti.mul_constcmp_mul_pos_right · cited by 0cmp_mul_pos_rightPartialOrder · cited by 6410PartialOrderStrictMono · cited by 706StrictMonoMonoidWithZero · cited by 456MonoidWithZeroMulPosStrictMono · cited by 94MulPosStrictMonomul_lt_mul_of_pos_right · cited by 54mul_lt_mul_of_pos_rightstrictMono_mul_right_of_posCITED BYCITES

Cites5

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Cited by3

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