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Proof step 114 from proof inv-get-inverse-succ (previous step)

# nσ = ⌜m⌝ + ⌜1⌝ , n1 < m, stutf(nσ), nσ[n1] ≤ nσ[m], ∀ m0. ¬ m < m0 ∧ nσ[m0] = nσ[n1] → ¬ n1 < m0 ⊦ nσ[n1 + 1] = nσ[n1] + 1, nσ[n1 + 1] = nσ[n1]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 115:
⊦ stutf(nσ) ↔ nσ ≠ [] ∧ nσ[0] = 0 ∧ (∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n + 1] = nσ[n] ∨ nσ[n + 1] = nσ[n] + 1)
Proof step 116:
# nσ = ⌜m⌝ + ⌜1⌝ , nσ[0] = 0, n1 < m, nσ[n1] ≤ nσ[m], ∀ m0. ¬ m < m0 ∧ nσ[m0] = nσ[n1] → ¬ n1 < m0, ∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n + 1] = nσ[n] ∨ nσ[n + 1] = nσ[n] + 1 ⊦ nσ[n1 + 1] = nσ[n1], nσ[n1 + 1] = nσ[n1] + 1, nσ = []

Rule argument

spec: <toplevel> 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: <all paths>

Additional information

Used terms: nσ