| ⌜nf0⌝ = (σ to n) + ⌜nf⌝ ⊦ nf0(n0 + n1 + n) = nf(n0 + n1), # σ < ⌜n⌝ |
⊦ σ0 = σ1 ↔ # σ0 = # σ1 ∧ (∀ n. ⌜n⌝ < # σ0 → σ0[n] = σ1[n])
# ⌜nf0⌝ = #((σ to n) + ⌜nf⌝ ) ∧ (∀ n0. ⌜n0⌝ < # ⌜nf0⌝ → ⌜nf0⌝ [n0] = ((σ to n) + ⌜nf⌝ )[n0]) ⊦ nf0(n0 + n1 + n) = nf(n0 + n1), # σ < ⌜n⌝
Used terms: (σ to n) + ⌜nf⌝ , ⌜nf0⌝