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Proof step 65 from proof leninv-succ (previous step)

nσ[(m1 + 1) + m] = nσ[m] + 1, # nσ = ∞, stutf(nσ) ⊦ nσ[m1 + m] = nσ[m] + 1 ∧ m1 ≠ 0, nσ[m] = nσ[m + 1], ∃ m0. m ≤ m0 ∧ ¬ m1 + m < m0 ∧ nσ[m] = nσ[m0] ∧ nσ[m0 + 1] = nσ[m0] + 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 66:
⊦ stutf(nσ) ↔ nσ ≠ [] ∧ nσ[0] = 0 ∧ (∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n + 1] = nσ[n] ∨ nσ[n + 1] = nσ[n] + 1)
Proof step 67:
nσ[(m1 + 1) + m] = nσ[m] + 1, # nσ = ∞, nσ ≠ [] ∧ nσ[0] = 0 ∧ (∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n + 1] = nσ[n] ∨ nσ[n + 1] = nσ[n] + 1) ⊦ nσ[m1 + m] = nσ[m] + 1 ∧ m1 ≠ 0, nσ[m] = nσ[m + 1], ∃ m0. m ≤ m0 ∧ ¬ m1 + m < m0 ∧ nσ[m] = nσ[m0] ∧ nσ[m0 + 1] = nσ[m0] + 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