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Proof step 6 from proof monls-append1 (previous step)

1 + n < # nl, mon<(⌜nl⌝ + ⌜nl0⌝ ), nl[n + 1] ≤ nl[n] ⊦ nl = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ mon<(nσ) ↔ (∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n] < nσ[n + 1])
Proof step 8:
1 + n < # nl, nl[n + 1] ≤ nl[n], ∀ n. ⌜n⌝ + ⌜1⌝ < #(⌜nl⌝ + ⌜nl0⌝ ) → (⌜nl⌝ + ⌜nl0⌝ )[n] < (⌜nl⌝ + ⌜nl0⌝ )[n + 1] ⊦ nl = []

Rule argument

spec: <toplevel> name: monls-def seq: ⊦ mon<(nσ) ↔ (∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n] < nσ[n + 1]) subst: [nσ] → [⌜nl⌝ + ⌜nl0⌝ ] flags: <all paths>

Additional information

Used terms: ⌜nl⌝ + ⌜nl0⌝