Theorem: Subtype.embeddingInsert_apply (Matroid/ForMathlib/Logic_Embedding_Set.lean)

State before:
α : Type u_1
β : Type u_2
γ : Type u_3
a : α
b : β
s : Set α
f✝ f : ↑s ↪ β
ha : a ∉ s
hb : b ∉ range ⇑f
⊢ (embeddingInsert f ha hb) ⟨a, ⋯⟩ = b
Tactic:
simp only [embeddingInsert, Embedding.coeFn_mk]
State after:
α : Type u_1
β : Type u_2
γ : Type u_3
a : α
b : β
s : Set α
f✝ f : ↑s ↪ β
ha : a ∉ s
hb : b ∉ range ⇑f
⊢ extend (inclusion ⋯) (⇑f) (fun x => b) ⟨a, ⋯⟩ = b

State before:
α : Type u_1
β : Type u_2
γ : Type u_3
a : α
b : β
s : Set α
f✝ f : ↑s ↪ β
ha : a ∉ s
hb : b ∉ range ⇑f
⊢ extend (inclusion ⋯) (⇑f) (fun x => b) ⟨a, ⋯⟩ = b
Tactic:
rw [extend_apply' _ _ _ (by simpa [embeddingOfSubset])]
State after:
no goals

State before:
α : Type u_1
β : Type u_2
γ : Type u_3
a : α
b : β
s : Set α
f✝ f : ↑s ↪ β
ha : a ∉ s
hb : b ∉ range ⇑f
⊢ ¬∃ a_1, inclusion ⋯ a_1 = ⟨a, ⋯⟩
Tactic:
simpa [embeddingOfSubset]
State after:
no goals