Theorems · Theorem · order theory

Set.AddAntidiagonal.eq_of_fst_eq_fst

∀ {α : Type u_1} [inst : AddCommMonoid α] [IsCancelAdd α] {s t : Set α} {a : α} {x y : ↑(s.antidiagonal t a)},
  (↑x).1 = (↑y).1 → x = y

Defined in: Mathlib.Data.Set.MulAntidiagonal
Cited by: 1 results in Mathlib
Foundations: Depth 8 from the axioms · uses no axioms
Assumes: AddCommMonoid IsCancelAdd

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

Setstatement and proof · cited by 53,352
AddCommMonoidstatement and proof · cited by 12,281
Set.Elemstatement and proof · cited by 7,166
IsCancelAddstatement and proof · cited by 79
Set.antidiagonalstatement and proof · cited by 11
Set.AddAntidiagonal.fst_eq_fst_iff_snd_eq_sndproof · cited by 2

Cited by1

Results whose statement or proof uses this declaration.

Set.AddAntidiagonal.eq_of_fst_le_fst_of_snd_le_sndproof · cited by 1