Theorems · Theorem · order theory

Pi.mabs_eq_one

∀ {ι : Type u_2} {α : ι → Type u_3} [inst : (i : ι) → Group (α i)] (f : (i : ι) → α i)
  [inst_1 : (i : ι) → LinearOrder (α i)] [∀ (i : ι), MulLeftMono (α i)] [∀ (i : ι), MulRightMono (α i)],
  |f|ₘ = 1 ↔ f = 1

Defined in: Mathlib.Algebra.Order.Group.Unbundled.Abs
Cited by: 0 results in Mathlib
Foundations: Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Group LinearOrder MulLeftMono MulRightMono

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LinearOrderstatement and proof · cited by 8,572
Groupstatement and proof · cited by 6,238
MulLeftMonostatement and proof · cited by 410
MulRightMonostatement and proof · cited by 263
mabsstatement and proof · cited by 148
mabs_oneproof · cited by 5

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