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Proof step 64 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, 1 + i1)), 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, 1 + i1), i→n(i1))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ i + j = j + i
Proof step 63:
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))

Rule argument

[x0lemmaarg: spec-name: int-basic2 instance-name: lemma-name: add-c antecedent: succedent: i + j = j + i substlist: [j, i] → [i1, 1] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 7, 1, 0, 1, 3)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (i1, 1)]]