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Proof step 10 from proof rem-preserves-monls (previous step)

np(# nl0), mon<(⌜nl0⌝ + ⌜m '⌝ ), ∀ nl1, np. # nl1 < #(nl0 + m ') → mon<(⌜nl1⌝ ) → mon<(rem(⌜nl1⌝ , np)) ⊦ mon<(rem(⌜nl0⌝ , np) + [])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
np(# nl0), mon<(⌜nl0⌝ + ⌜m '⌝ ), ∀ nl1, np. # nl1 < #(nl0 + m ') → mon<(⌜nl1⌝ ) → mon<(rem(⌜nl1⌝ , np)) ⊦ mon<(rem(⌜nl0⌝ , np))

Rule argument

Additional information

Used simplifier rules: append-assoc: ⊦ (nσ + nσ0) + nσ1 = nσ + nσ0 + nσ1; from specification stream[natstream]%append-empty: ⊦ nσ + [] = nσ; from specification stream[natstream]