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Proof step 28 from proof rem-preserves-monls (previous step)

mon<(⌜nl0⌝ + ⌜m '⌝ ), ⌜n⌝ < # rem(⌜nl0⌝ , np), rem(⌜nl0⌝ , np)[n + 1] ≤ rem(⌜nl0⌝ , np)[n], ⌜n⌝ + ⌜1⌝ < # rem(⌜nl0⌝ , np), ∀ n. ⌜n⌝ + ⌜1⌝ < # rem(⌜nl0⌝ , np) → rem(⌜nl0⌝ , np)[n] < rem(⌜nl0⌝ , np)[n + 1], ∀ nl1, np. # nl1 < #(nl0 + m ') → mon<(⌜nl1⌝ ) → mon<(rem(⌜nl1⌝ , np)) ⊦ np(# nl0)

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 5 terms: n

Additional information

Used simplifier rules: le-ls-simp: ⊦ m ≤ n → (n < m ↔ false); from specification nat Used terms: n