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Proof step 84 from proof inv-get-inverse-succ (previous step)

# nσ = ∞, nσ[m + 1] = nσ[m] + 1, stutf(nσ), nσ[n1] ≤ nσ[m], ∀ m. nσ[m] = nσ[n1] → ¬ n1 < m ⊦ nσ[n1 + 1] = nσ[n1] + 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 85:
⊦ stutf(nσ) ↔ nσ ≠ [] ∧ nσ[0] = 0 ∧ (∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n + 1] = nσ[n] ∨ nσ[n + 1] = nσ[n] + 1)
Proof step 86:
# nσ = ∞, nσ[m + 1] = nσ[m] + 1, nσ ≠ [] ∧ nσ[0] = 0 ∧ (∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n + 1] = nσ[n] ∨ nσ[n + 1] = nσ[n] + 1), nσ[n1] ≤ nσ[m], ∀ m. nσ[m] = nσ[n1] → ¬ n1 < m ⊦ nσ[n1 + 1] = nσ[n1] + 1

Rule argument

spec: inst: name: stutf-def seq: ⊦ stutf(nσ) ↔ nσ ≠ [] ∧ nσ[0] = 0 ∧ (∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n + 1] = nσ[n] ∨ nσ[n + 1] = nσ[n] + 1) subst: [nσ] → [nσ] flags: rewrite, current

Additional information

Used terms: nσ