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Proof step 6 from proof stutf-slowincrease (previous step)

stutf(nσ), nσ[m] + n0 + 1 < nσ[m + n0 + 1], ⌜m⌝ + ⌜n0⌝ + ⌜1⌝ < # nσ, ⌜m⌝ + ⌜n0⌝ < # nσ, nσ[m + n0] ≤ nσ[m] + n0 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ stutf(nσ) ↔ nσ ≠ [] ∧ nσ[0] = 0 ∧ (∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n + 1] = nσ[n] ∨ nσ[n + 1] = nσ[n] + 1)
Proof step 8:
nσ ≠ [] ∧ nσ[0] = 0 ∧ (∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n + 1] = nσ[n] ∨ nσ[n + 1] = nσ[n] + 1), nσ[m] + n0 + 1 < nσ[m + n0 + 1], ⌜m⌝ + ⌜n0⌝ + ⌜1⌝ < # nσ, ⌜m⌝ + ⌜n0⌝ < # nσ, nσ[m + n0] ≤ nσ[m] + n0 ⊦

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