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Theorems · Theorem · order theory

zsmul_strictMono_right

∀ (α : Type u_1) [inst : AddCommGroup α] [inst_1 : PartialOrder α] [IsOrderedAddMonoid α] {n : ℤ},
  0 < n → StrictMono fun x => n • x
Defined in
Mathlib.Algebra.Order.Group.Basic
Cited by
3 results in Mathlib
Foundations
Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommGroupPartialOrderIsOrderedAddMonoid
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Around this declaration

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

zsmul_lt_zsmul_right · cited by 1zsmul_lt_zsmul_rightzsmul_le_zsmul_iff_right · cited by 0zsmul_le_zsmul_iff_rightzsmul_lt_zsmul_iff_right · cited by 0zsmul_lt_zsmul_iff_rightAddCommGroup · cited by 12871AddCommGroupPartialOrder · cited by 6410PartialOrderIsOrderedAddMonoid · cited by 1659IsOrderedAddMonoidStrictMono · cited by 706StrictMonosub_pos · cited by 147sub_poszsmul_sub · cited by 3zsmul_subzsmul_pos · cited by 1zsmul_poszsmul_strictMono_rightCITED BYCITES

Cites7

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Cited by3

Results whose statement or proof uses this declaration.