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Proof step 6 from proof rem-preserves-monls (previous step)

mon<(⌜nl⌝ ), ∀ nl0, np. # nl0 < # nl → mon<(⌜nl0⌝ ) → mon<(rem(⌜nl0⌝ , np)) ⊦ nl = [], mon<(rem(⌜nl⌝ , np))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ nl ≠ [] ↔ (∃ nl0, m. nl = nl0 + m ')
Proof step 8:
mon<(⌜nl⌝ ), ∀ nl0, np. # nl0 < # nl → mon<(⌜nl0⌝ ) → mon<(rem(⌜nl0⌝ , np)) ⊦ ∀ nl0, m. nl ≠ nl0 + m ', mon<(rem(⌜nl⌝ , np))

Rule argument

spec: list inst: natstream name: lastdiv-rew seq: ⊦ nl ≠ [] ↔ (∃ nl0, m. nl = nl0 + m ') subst: [nl] → [nl] flags: rewrite

Additional information

Used terms: nl