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Proof step 4 from proof read-get (previous step)

n ≤ # ax0, ∀ n, fs. n < # ax0 → fs[ax0][n] = fs[ax0[n]] ∨ ax0 = [] ⊦ (fs[adr] ' + fs[ax0])[n] = fs[(adr ' + ax0)[n]]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ ¬ n < # ndx → (ndx + ndx0)[n] = ndx0[n - # ndx]
Proof step 6:
n ≤ # ax0, ∀ n, fs. n < # ax0 → fs[ax0][n] = fs[ax0[n]] ∨ ax0 = [] ⊦ fs[ax0][n - # fs[adr] '] = fs[(adr ' + ax0)[n]], n < # fs[adr] '

Rule argument

spec: list-del, inst: node-list name: get-append-grt seq: ⊦ ¬ n < # ndx → (ndx + ndx0)[n] = ndx0[n - # ndx] subst: [n, ndx0, ndx] → [n, fs[ax0], fs[adr] '] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n < # ndx → (ndx + ndx0)[n] = ndx[n]; (s)%a: ⊦ (ndx + ndx0) + ndx1 = ndx + ndx0 + ndx1; from specification list[node-list]% ⊦ # nd ' = 0 +1; (s)% ⊦ m < 1 ↔ m = 0; (s)% ⊦ nd '[0] = nd; (s)% ⊦ (adr ' + ax)[0] = adr; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set] Used terms: n, fs[ax0], fs[adr] '