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Proof step 5 from proof monls-append2 (previous step)

∀ n. 1 + n < # nl0 + # nl → (nl + nl0)[n] < (nl + nl0)[n + 1] ⊦ mon<(⌜nl0⌝ )

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ mon<(nσ) ↔ (∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n] < nσ[n + 1])
Proof step 7:
∀ n. 1 + n < # nl0 + # nl → (nl + nl0)[n] < (nl + nl0)[n + 1] ⊦ ∀ n. ⌜n⌝ + ⌜1⌝ < # ⌜nl0⌝ → ⌜nl0⌝ [n] < ⌜nl0⌝ [n + 1]

Rule argument

spec: inst: name: monls-def seq: ⊦ mon<(nσ) ↔ (∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n] < nσ[n + 1]) subst: [nσ] → [⌜nl0⌝ ] flags: rewrite, current

Additional information

Used terms: ⌜nl0⌝