Theorems · Theorem · logic and foundations
Cardinal.toNat_eq_of_forall_le_iff
∀ {c : Cardinal.{u}} {d : Cardinal.{v}}, (∀ (n : ℕ), ↑n ≤ c ↔ ↑n ≤ d) → Cardinal.toNat c = Cardinal.toNat dA Cardinal.toNat version of eq_of_forall_le_iff.
This is useful for proving equality of Module.finrank.
- Defined in
- Mathlib.SetTheory.Cardinal.ToNat
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Cardinalstatement and proof · cited by 2,598
- MonoidWithZeroHomstatement · cited by 704
- Cardinal.aleph0proof · cited by 521
- not_leproof · cited by 328
- Cardinal.toNatstatement and proof · cited by 153
- eq_of_forall_le_iffproof · cited by 65
- Cardinal.cast_toNat_of_lt_aleph0proof · cited by 9
- Cardinal.toNat_apply_of_aleph0_leproof · cited by 9
- iff_iff_and_or_not_and_notproof · cited by 3
- Cardinal.aleph0_leproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- IsFractionRing.finrank_left_eqproof · cited by 1