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Theorems · Theorem · order theory

Right.inv_nonneg

∀ {G₀ : Type u_3} [inst : GroupWithZero G₀] [inst_1 : PartialOrder G₀] [MulPosReflectLT G₀] {a : G₀}, 0 ≤ a⁻¹ ↔ 0 ≤ a
Defined in
Mathlib.Algebra.Order.GroupWithZero.Basic
Cited by
2 results in Mathlib
Foundations
Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
GroupWithZeroPartialOrderMulPosReflectLT
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Around this declaration

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

div_le_div_of_nonneg_right · cited by 77div_le_div_of_nonneg_rightdiv_nonpos_of_nonpos_of_nonneg · cited by 0div_nonpos_of_nonpos_of_n…PartialOrder · cited by 6410PartialOrderGroupWithZero · cited by 691GroupWithZeroMulPosReflectLT · cited by 93MulPosReflectLTRight.inv_nonnegCITED BYCITES

Cites3

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Cited by2

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