/- Copyright 2025 The Formal Conjectures Authors. Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at https://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. -/ module public import Mathlib.Data.Finset.Powerset@[expose] public sectionnamespace Finsetvariable {α : Type*} [DecidableEq α] {s t : Finset α} {n : ℕ}attribute [gcongr] powersetCard_monolemma powersetCard_inter : powersetCard n (s ∩ t) = powersetCard n s ∩ powersetCard n t := byα:Type u_1inst✝:DecidableEq αs:Finset αt:Finset αn:ℕ⊢ powersetCard n (s ∩ t) = powersetCard n s ∩ powersetCard n t extα:Type u_1inst✝:DecidableEq αs:Finset αt:Finset αn:ℕa✝:Finset α⊢ a✝ ∈ powersetCard n (s ∩ t) ↔ a✝ ∈ powersetCard n s ∩ powersetCard n t; simpa [subset_inter_iff] using and_and_rightAll goals completed! 🐙@[simp] lemma disjoint_powersetCard_powersetCard : Disjoint (powersetCard n s) (powersetCard n t) ↔ #(s ∩ t) < n := byα:Type u_1inst✝:DecidableEq αs:Finset αt:Finset αn:ℕ⊢ Disjoint (powersetCard n s) (powersetCard n t) ↔ #(s ∩ t) < n simp [disjoint_iff_inter_eq_empty, ← powersetCard_inter]All goals completed! 🐙end Finset