Theorems · Theorem · order theory

Pi.abs_eq_zero

∀ {ι : Type u_2} {α : ι → Type u_3} [inst : (i : ι) → AddGroup (α i)] (f : (i : ι) → α i)
  [inst_1 : (i : ι) → LinearOrder (α i)] [∀ (i : ι), AddLeftMono (α i)] [∀ (i : ι), AddRightMono (α i)], |f| = 0 ↔ f = 0

Defined in: Mathlib.Algebra.Order.Group.Unbundled.Abs
Cited by: 0 results in Mathlib
Foundations: Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AddGroup LinearOrder AddLeftMono AddRightMono

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

LinearOrderstatement and proof · cited by 8,572
AddGroupstatement and proof · cited by 4,410
absstatement and proof · cited by 1,814
AddLeftMonostatement and proof · cited by 687
AddRightMonostatement and proof · cited by 367
abs_zeroproof · cited by 88
abs_eq_zeroproof · cited by 17

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