Theorems · Theorem · logic and foundations

Set.exists_eq_insert_iff_ncard

∀ {α : Type u_1} {s t : Set α},
  autoParam s.Finite Set.exists_eq_insert_iff_ncard._auto_1 →
    ((∃ a ∉ s, insert a s = t) ↔ s ⊆ t ∧ s.ncard + 1 = t.ncard)

Defined in: Mathlib.Data.Set.Card
Cited by: 0 results in Mathlib
Foundations: Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

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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
Finset.cardproof · cited by 2,327
Set.Finitestatement and proof · cited by 1,814
Set.Finite.toFinsetproof · cited by 351
Set.ncardstatement and proof · cited by 344
Set.Infiniteproof · cited by 263
Set.finite_or_infiniteproof · cited by 23
Set.ncard_eq_toFinset_cardproof · cited by 21
Set.Infinite.ncardproof · cited by 12
Set.Finite.insertproof · cited by 11
Finset.exists_eq_insert_iffproof · cited by 3
Set.Finite.toFinset_subset_toFinsetproof · cited by 2

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