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Theorems · Theorem · order theory

StrictAnti.const_smul

∀ {α : Type u_1} {β : Type u_2} {a : α} [inst : SMul α β] [inst_1 : Preorder α] [inst_2 : Preorder β] [inst_3 : Zero α]
  [PosSMulStrictMono α β] {γ : Type u_3} [inst_5 : Preorder γ] {f : γ → β},
  StrictAnti f → 0 < a → StrictAnti fun x => a • f x

Scalar multiplication on the left by a positive element preserves strict antitonicity.

Defined in
Mathlib.Algebra.Order.Module.Defs
Cited by
0 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
SMulPreorderPreorderZeroPosSMulStrictMonoPreorder
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Preorder · cited by 7952PreorderStrictAnti · cited by 204StrictAntiPosSMulStrictMono · cited by 128PosSMulStrictMonoStrictMono.comp_strictAnti · cited by 6StrictMono.comp_strictAntistrictMono_smul_left_of_pos · cited by 3strictMono_smul_left_of_p…StrictAnti.const_smulCITED BYCITES

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