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Theorems · Theorem · order theory

strictMono_smul_left_of_pos

∀ {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], 0 < a → StrictMono fun x => a • x
Defined in
Mathlib.Algebra.Order.Module.Defs
Cited by
3 results in Mathlib
Foundations
Depth 5 from the axioms · uses no axioms
Assumes
SMulPreorderPreorderZeroPosSMulStrictMono
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Around this declaration

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

smul_lt_smul_of_pos_left · cited by 23smul_lt_smul_of_pos_leftStrictMono.const_smul · cited by 0StrictMono.const_smulStrictAnti.const_smul · cited by 0StrictAnti.const_smulPreorder · cited by 7952PreorderStrictMono · cited by 706StrictMonoPosSMulStrictMono · cited by 128PosSMulStrictMonoPosSMulStrictMono.smul_lt_smul_of_pos_left · cited by 1PosSMulStrictMono.smul_lt…strictMono_smul_left_of_posCITED BYCITES

Cites4

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Cited by3

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