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Proof step 63 from proof push-corr (previous step)

0 ≤ i1, 0 ≤ (i0 + i1) % n→i(# ar), 0 ≤ i0, i1 ≤ n→i(# ar), i0 < n→i(# ar), inv(mk(ar, n→i(# ar), i0, i1)), i1 < n→i(# ar), inv(mk(ar[(i→n(i0) + i→n(i1)) % # ar, a], n→i(# ar), i0, i1 + 1)), 0 ≤ i0 + i1 ⊦ # ar = 0, tolist(mk(ar, n→i(# ar), i0, i1), i→n(i1)) = tolist(mk(ar[(i→n(i0) + i→n(i1)) % # ar, a], n→i(# ar), i0, i1 + 1), i→n(i1))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ x0 = x1 ↔ # x0 = # x1 ∧ (∀ n. n < # x0 → x0[n] = x1[n])
Proof step 62:
0 ≤ i1, 0 ≤ (i0 + i1) % n→i(# ar), 0 ≤ i0, i1 ≤ n→i(# ar), i0 < n→i(# ar), inv(mk(ar, n→i(# ar), i0, i1)), i1 < n→i(# ar), inv(mk(ar[(i→n(i0) + i→n(i1)) % # ar, a], n→i(# ar), i0, i1 + 1)), 0 ≤ i0 + i1 ⊦ # ar = 0, # tolist(mk(ar, n→i(# ar), i0, i1), i→n(i1)) = # tolist(mk(ar[(i→n(i0) + i→n(i1)) % # ar, a], n→i(# ar), i0, i1 + 1), i→n(i1)) ∧ (∀ n. n < # tolist(mk(ar, n→i(# ar), i0, i1), i→n(i1)) → (tolist(mk(ar, n→i(# ar), i0, i1), i→n(i1))[n]) = (tolist(mk(ar[(i→n(i0) + i→n(i1)) % # ar, a], n→i(# ar), i0, i1 + 1), i→n(i1))[n]))

Rule argument

[x0lemmaarg: spec-name: list-del instance-name: queue lemma-name: extension antecedent: succedent: x0 = x1 ↔ # x0 = # x1 ∧ (∀ n. n < # x0 → x0[n] = x1[n]) substlist: [x1, x0] → [tolist (mk (ar[(i→n(i0) + i→n(i1)) % # ar, a], n→i(# ar), i0, i1 + 1), i→n(i1)), tolist(mk(ar, n→i(# ar), i0, i1), i→n(i1))] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 1)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (tolist (mk (ar[(i→n(i0) + i→n(i1)) % # ar, a], n→i(# ar), i0, i1 + 1), i→n(i1)), tolist(mk(ar, n→i(# ar), i0, i1), i→n(i1)))]]