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Proof step 13 from proof inv-inverts (previous step)

nσ[n + 1] = nσ[n] + 1, leninv(nσ) = ⌜0⌝ , max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]) = ⌜n⌝ , ⌜n⌝ + ⌜1⌝ < # nσ, stutf(nσ) ⊦ ([])[nσ[n]] = n

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: leninv-zero seq: ⊦ stutf(nσ) → (leninv(nσ) = ⌜0⌝ ↔ nσ = ⌜λ n. 0⌝ ) subst: [nσ] → [nσ] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ⌜nnf⌝ [n] = nnf(n); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: nσ