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Proof step 15 from proof to-to-leq-inf (previous step)

∀ m, nf. m ≤ n0 → (nf to n0) to m = nf to m ⊦ ((nf to n0) to n0) + ((nf to n0) + nf(n0) ')[n0] ' = nf to n0 + 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ ¬ n < # x → (x + y)[n] = y[n - # x]
Proof step 17:
¬ n0 < #(nf to n0), ∀ m, nf. m ≤ n0 → (nf to n0) to m = nf to m ⊦ ((nf to n0) to n0) + nf(n0) '[n0 - #(nf to n0)] ' = nf to n0 + 1

Rule argument

spec: list-del inst: name: get-append-grt seq: ⊦ ¬ n < # x → (x + y)[n] = y[n - # x] subst: [n, y, x] → [n0, nf(n0) ', nf to n0] flags: rewrite

Additional information

Used simplifier rules: size-inf-to: ⊦ #(nf to n) = n;%get-butlast: ⊦ n < # x → (x + a ')[n] = x[n]; from specification list-del%a: ⊦ (x + y) + z = x + y + z; from specification list%ref-1: ⊦ ¬ n < n; from specification nat-basic1 Used terms: n0, nf(n0) ', nf to n0