Theorem: LO.FirstOrder.Arith.Model.mem_inter_iff (Arithmetization/ISigmaOne/HFS/Basic.lean)

State before:
M : Type u_1
inst✝⁵ : Zero M
inst✝⁴ : One M
inst✝³ : Add M
inst✝² : Mul M
inst✝¹ : LT M
inst✝ : M ⊧ₘ* 𝐈𝚺₁
a b c : M
⊢ a ∈ b ∩ c ↔ a ∈ b ∧ a ∈ c
Tactic:
simp [Inter.inter, inter, mem_sInter_iff_of_pos (s := {b, c}) (nonempty_iff.mpr ⟨b, by simp⟩)]
State after:
no goals

State before:
M : Type u_1
inst✝⁵ : Zero M
inst✝⁴ : One M
inst✝³ : Add M
inst✝² : Mul M
inst✝¹ : LT M
inst✝ : M ⊧ₘ* 𝐈𝚺₁
a b c : M
⊢ b ∈ {b, c}
Tactic:
simp
State after:
no goals