mathlib3
10da8e67 - feat(set_theory/cardinal,*): assorted lemmas (#9516)

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4 years ago
feat(set_theory/cardinal,*): assorted lemmas (#9516) ### New instances * a denumerable type is infinite; * `Prop` is (noncomputably) enumerable; * `Prop` is nontrivial; * `cardinal.can_lift_cardinal_Type`: lift `cardinal.{u}` to `Type u`. ### New lemmas / attrs * `quotient.out_equiv_out` : `x.out ≈ y.out ↔ x = y`; * `quotient.out_inj` : `x.out = y.out ↔ x = y`; * `cardinal.lift_bit0`, `cardinal.lift_bit1`, `cardinal.lift_two`, `cardinal.lift_prod` : new lemmas about `cardinal.lift`; * `cardinal.omega_le_lift` and `cardinal.lift_le_omega` : simplify `ω ≤ lift c` and `lift c ≤ ω`; * `cardinal.omega_le_add_iff`, `cardinal.encodable_iff`, `cardinal.mk_le_omega`, `cardinal.mk_denumerable`: new lemmas about `cardinal.omega`; * add `@[simp]` attribute to `cardinal.mk_univ`, add `cardinal.mk_insert`; * generalize `cardinal.nat_power_eq` to `cardinal.power_eq_two_power` and `cardinal.prod_eq_two_power`.
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