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Proof step 61 from proof push-corr (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
m ≠ n ⊦ (ar[m, a][n]) = ar[n]
Proof step 60:
¬ (i→n(i0) + i→n(i1)) % # ar ≠ (i→n(i0) + n) % # ar, 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, n < i→n(i1), 0 < i1 ⊦ i1 = 0, # ar = 0, ar[(i→n(i0) + n) % # ar] = (ar[(i→n(i0) + i→n(i1)) % # ar, a][(i→n(i0) + n) % # ar]), # ar = 1

Rule argument

[x0lemmaarg: spec-name: array instance-name: lemma-name: cngetput antecedent: m ≠ n succedent: (ar[m, a][n]) = ar[n] substlist: [n, a, m, ar] → [(i→n(i0) + n) % # ar, a, (i→n(i0) + i→n(i1)) % # ar, ar] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 2, 1, 1)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + n = n + m])], [EXTRATERMS : ((i→n(i0) + n) % # ar, a, (i→n(i0) + i→n(i1)) % # ar, ar)]]