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Theorems · Theorem · order theory

mabs_ne_one

∀ {α : Type u_1} [inst : Group α] [inst_1 : LinearOrder α] [MulLeftMono α] {a : α} [MulRightMono α], |a|ₘ ≠ 1 ↔ a ≠ 1
Defined in
Mathlib.Algebra.Order.Group.Unbundled.Abs
Cited by
1 results in Mathlib
Foundations
Depth 30 from the axioms · uses propext, Quot.sound
Assumes
GroupLinearOrderMulLeftMonoMulRightMono
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Around this declaration

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

mabs_eq_one · cited by 2mabs_eq_oneLinearOrder · cited by 8572LinearOrderGroup · cited by 6238GroupMulLeftMono · cited by 410MulLeftMonoMulRightMono · cited by 263MulRightMonomabs · cited by 148mabsLE.le.lt_iff_ne' · cited by 16le.lt_iff_ne'one_le_mabs · cited by 11one_le_mabsone_lt_mabs · cited by 6one_lt_mabsmabs_ne_oneCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.