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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)) ⊦ mon<(rem(⌜nl⌝ , np))

User applied rule cut formula

And obtained the following new goals

Proof step 7:
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: ⊦ ⌜[]⌝ = []; (s)% ⊦ rem([], np) = []; (s) Used formulas: nl = []