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Proof step 65 from proof push-corr (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 64:
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))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (x0 + x1) + x2 = x0 + x1 + x2], [CSIMPSEQ : ⊦ x0 + x1 = x2 + x1 ↔ x0 = x2], [CSIMPSEQ : m < # ar ⊦ (ar[m, a][m]) = a], [CSIMPSEQ : n ≠ 0 ⊦ m % n < n], [CSIMPSEQ : ⊦ m + n = n + m])]]