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Proof step 5 from proof key-cons-ext (previous step)

key-cons(ndx0), key-cons(nd.key, nd), n ≤ # ndx0, ∀ n. n < # ndx0 → key-cons(ndx0[n].key, ndx0[n]) ⊦ key-cons((nd ' + ndx0)[n].key, (nd ' + ndx0)[n])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ ¬ n < # ndx → (ndx + ndx0)[n] = ndx0[n - # ndx]
Proof step 7:
key-cons(nd.key, nd), key-cons(ndx0), n ≤ # ndx0, ∀ n. n < # ndx0 → key-cons(ndx0[n].key, ndx0[n]) ⊦ n < # nd ', key-cons(ndx0[n - # nd '].key, ndx0[n - # nd '])

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, ndx0, nd '] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # nd ' = 0 +1; (s)% ⊦ m < 1 ↔ m = 0; (s)% ⊦ 0 ≤ m; (s)% ⊦ (nd ' + ndx)[0] = nd; (s)%a: ⊦ (ndx + ndx0) + ndx1 = ndx + ndx0 + ndx1; from specification list[node-list] Used terms: n, ndx0, nd '