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Proof step 2 from proof monls-append1 (previous step)

mon<(⌜nl⌝ + ⌜nl0⌝ ) ⊦ mon<(⌜nl⌝ )

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ mon<(nσ) ↔ (∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n] < nσ[n + 1])
Proof step 4:
mon<(⌜nl⌝ + ⌜nl0⌝ ) ⊦ ∀ n. ⌜n⌝ + ⌜1⌝ < # ⌜nl⌝ → ⌜nl⌝ [n] < ⌜nl⌝ [n + 1]

Rule argument

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

Additional information

Used terms: ⌜nl⌝