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Proof step 5 from proof rem-preserves-monls (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 6:
mon<(⌜nl⌝ ), ∀ nl0, np. # nl0 < # nl → mon<(⌜nl0⌝ ) → mon<(rem(⌜nl0⌝ , np)) ⊦ nl = [], mon<(rem(⌜nl⌝ , np))

Rule argument

fma: nl = []

Additional information

Used simplifier rules: empty: ⊦ ⌜[]⌝ = []; from specification stream[natstream]%rem-base: ⊦ rem([], np) = []; from specification mon-lim-filter-count[natstream] Used formulas: nl = []