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Proof step 8 from proof rem-preserves-monls (previous step)

mon<(⌜nl⌝ ), ∀ nl0, np. # nl0 < # nl → mon<(⌜nl0⌝ ) → mon<(rem(⌜nl0⌝ , np)) ⊦ ∀ nl0, m. nl ≠ nl0 + m ', mon<(rem(⌜nl⌝ , np))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
mon<(⌜nl0⌝ + ⌜m '⌝ ), ∀ nl1, np. # nl1 < #(nl0 + m ') → mon<(⌜nl1⌝ ) → mon<(rem(⌜nl1⌝ , np)) ⊦ mon<(rem(⌜nl0⌝ , np) + (np(# nl0) ⊃ [];⌜m '⌝ ))

Rule argument

Additional information

Used simplifier rules: append-assoc: ⊦ (nσ + nσ0) + nσ1 = nσ + nσ0 + nσ1; from specification stream[natstream]%rem-rec: ⊦ rem(⌜nl⌝ + ⌜m '⌝ , np) = rem(⌜nl⌝ , np) + (np(# nl) ⊃ [];⌜m '⌝ ); from specification mon-lim-filter-count[natstream]%a: ⊦ (nl + nl0) + nl1 = nl + nl0 + nl1; from specification list[natstream]%append-finfin: ⊦ ⌜nl + nl0⌝ = ⌜nl⌝ + ⌜nl0⌝ ; from specification stream[natstream]