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Proof step 11 from proof monls-append1 (previous step)

1 + n < # nl, (nl + nl0)[n] < nl[n + 1], (nl + nl0)[n] < nl[n], nl[n + 1] ≤ nl[n] ⊦ nl = []

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: list-del, inst: natstream name: get-append-less seq: ⊦ n < # nl → (nl + nl0)[n] = nl[n] subst: [n, nl0, nl] → [n, nl0, nl] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ ¬ m < n → ¬ m + m0 < n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: n, nl0, nl