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Proof step 9 from proof rem-preserves-monls (previous step)

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

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Proof step 10:
np(# nl0), mon<(⌜nl0⌝ + ⌜m '⌝ ), ∀ nl1, np. # nl1 < #(nl0 + m ') → mon<(⌜nl1⌝ ) → mon<(rem(⌜nl1⌝ , np)) ⊦ mon<(rem(⌜nl0⌝ , np) + [])
Proof step 12:
¬ np(# nl0), mon<(⌜nl0⌝ + ⌜m '⌝ ), ∀ nl1, np. # nl1 < #(nl0 + m ') → mon<(⌜nl1⌝ ) → mon<(rem(⌜nl1⌝ , np)) ⊦ mon<(rem(⌜nl0⌝ , np) + ⌜m '⌝ )

Rule argument

pos: right 1

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