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refactor(set_theory/cardinal): swap sides of
simp
lemmas (#10040)
## API changes ### Swap sides of simp lemmas - `cardinal.add_def` is no loner a `simp` lemma, `cardinal.mk_sum` (renamed from `cardinal.add`) simplifies `#(α ⊕ β)` to `lift.{v u} (#α) + lift.{u v} (#β)`; - `cardinal.mul_def` is no loner a `simp` lemma, `cardinal.mk_prod` (merged with `cardinal.mul`) simplifies `#(α × β)` to `lift.{v u} (#α) * lift.{u v} (#β)`; - `cardinal.power_def` is no longer a `simp` lemma. New lemma `cardinal.mk_arrow` computes `#(α → β)`. It is not a `simp` lemma because it follows from other `simp` lemmas. - replace `cardinal.sum_mk` with `cardinal.mk_sigma` and `cardinal.prod_mk` with `cardinal.mk_pi`; ### Other changes - new lemmas `@[simp] cardinal.lift_uzero` and `cardinal.lift_umax'`; - split `cardinal.linear_order` into `cardinal.preorder` (doesn't rely on `classical.choice`), `cardinal.partial_order` (needs `classical.choice`, computable), and `cardinal.linear_order` (noncomputable); - add `cardinal.lift_order_embedding`; - add `cardinal.mk_psum`; - rename `cardinal.prop_eq_two` to `cardinal.mk_Prop`, drop the old `mk_Prop`; - use local notation for natural power; - rename old `sum_const` to `sum_const'`, the new `@[simp] lemma sum_const` is what used to be `sum_const_eq_lift_mul`; - rename old `prod_const` to `prod_const'`, the new `@[simp] lemma prod_const` deals with types in different universes; - add `@[simp]` to `cardinal.prod_eq_zero` and `cardinal.omega_le_mk`; - add `@[simp]` lemmas `cardinal.mk_eq_one`, `cardinal.mk_vector`, `cardinal.omega_mul_eq`, and `cardinal.mul_omega_eq`; - replace `mk_plift_of_true` and `mk_plift_of_false` with `mk_plift_true` and `mk_plift_false`; - `mk_list_eq_mk` and `mk_finset_eq_mk` now assume `[infinite α]` instead of `ω ≤ #α`.
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