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Proof step 47 from proof inv-inverts (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: monle-leq seq: ⊦ mon≤(nσ) ∧ m ≤ n ∧ ⌜n⌝ < # nσ → nσ[m] ≤ nσ[n] subst: [nσ, m, n] → [nσ, n + 1, n0]

Additional information

Used simplifier rules: stutf-monle: ⊦ stutf(nσ) → (mon≤(nσ) ↔ true);% ⊦ m + 1 ≤ n ↔ m < n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ ¬ n < n; (s)% ⊦ ¬ m < n → ¬ m + m0 < n; (s) Used terms: nσ, n + 1, n0