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Proof step 2 from proof stutf-invmonls (previous step)

stutf(nσ) ⊦ mon<(inv(nσ))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: monls-def seq: ⊦ mon<(nσ) ↔ (∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n] < nσ[n + 1]) subst: [nσ] → [inv(nσ)] flags: rewrite, current

Additional information

Used simplifier rules: leninv-is-len-inv: ⊦ stutf(nσ) → # inv(nσ) = leninv(nσ);%inv-ls-notleq: ⊦ stutf(nσ) ∧ ⌜n⌝ + ⌜1⌝ < leninv(nσ) → (inv(nσ)[n + 1] ≤ inv(nσ)[n] ↔ false);%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat%add-assoc: ⊦ (n∞ + n∞1) + n∞2 = n∞ + n∞1 + n∞2; from specification nat-inf%add-comm: ⊦ n∞1 + n∞2 = n∞2 + n∞1; from specification nat-inf%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2 Used terms: inv(nσ)