Theorem: LO.FirstOrder.Arith.Model.ppow2_defined (Arithmetization/ISigmaZero/Exponential/PPow2.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* 𝐈𝚫₀
⊢ 𝚺₀-Predicate PPow2 via ppow2Def
Tactic:
intro v
State after:
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* 𝐈𝚫₀
v : Fin 1 → M
⊢ (fun v => PPow2 (v 0)) v ↔ (Semiformula.Evalbm M v) (HSemiformula.val ppow2Def)

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* 𝐈𝚫₀
v : Fin 1 → M
⊢ (fun v => PPow2 (v 0)) v ↔ (Semiformula.Evalbm M v) (HSemiformula.val ppow2Def)
Tactic:
simp[PPow2, ppow2Def, Matrix.vecHead, Matrix.vecTail,
lenbit_defined.df.iff, pow2_defined.df.iff, sppow2_defined.df.iff, numeral_eq_natCast]
State after:
no goals