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Require simp to make progress.

finite-set-exercises
Joshua Potter 2023-09-08 18:50:44 -06:00
parent b9b54fce14
commit 7e1eb8fdfb
1 changed files with 0 additions and 2 deletions
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Bookshelf/Enderton/Set/Chapter_3.lean
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@ -86,7 +86,6 @@ theorem theorem_3h_dom {F : Set.HRelation β γ} {G : Set.HRelation α β}
simp only [Set.mem_setOf_eq] simp only [Set.mem_setOf_eq]
have ⟨z, hz⟩ := dom_exists ht have ⟨z, hz⟩ := dom_exists ht
refine ⟨dom_comp_imp_dom_self ht, ?_⟩ refine ⟨dom_comp_imp_dom_self ht, ?_⟩
simp only [Set.mem_setOf_eq] at hz
have ⟨a, ha⟩ := hz have ⟨a, ha⟩ := hz
unfold dom unfold dom
simp only [Set.mem_image, Prod.exists, exists_and_right, exists_eq_right] simp only [Set.mem_image, Prod.exists, exists_and_right, exists_eq_right]
@ -675,7 +674,6 @@ theorem exercise_3_5b {A : Set α} (B : Set β)
apply And.intro apply And.intro
· show ∀ t, t ∈ Set.prod A B → t ∈ ⋃₀ {Set.prod {x} B | x ∈ A} · show ∀ t, t ∈ Set.prod A B → t ∈ ⋃₀ {Set.prod {x} B | x ∈ A}
intro t h intro t h
simp only [Set.mem_setOf_eq] at h
unfold Set.sUnion sSup Set.instSupSetSet unfold Set.sUnion sSup Set.instSupSetSet
simp only [Set.mem_setOf_eq, exists_exists_and_eq_and] simp only [Set.mem_setOf_eq, exists_exists_and_eq_and]
unfold Set.prod at h unfold Set.prod at h