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Proof step 53 from proof push-corr (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 52:
(i→n(i0) + i→n(i1) - # ar) % # ar = (i→n(i0) + n) % # ar, # ar ≤ i→n(i0) + i→n(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) + n) % # ar, a], n→i(# ar), i0, i1 + 1)), 0 ≤ i0 + i1, n < i→n(i1), 0 < i1 ⊦ # ar = 0, ar[(i→n(i0) + n) % # ar] = a, # ar = 1, i1 = 0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]