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Proof step 23 from proof push-corr (previous step)

¬ (i→n(i0) ≤ # ar ∧ i→n(i1) < # ar), n0 % # ar = (i→n(i0) + n) % # ar, i→n(i0) + i→n(i1) = n0 + # ar, 0 < i1, n < i→n(i1), 0 ≤ i0 + i1, inv(mk(ar[n0 % # 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 ≤ n0 ⊦ i→n(i0) + i→n(i1) < # ar + # ar, i1 = 0, # ar = 1, ar[n0 % # ar] = a, # ar = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
i→n(i0) + i→n(i1) = n0 + # ar, n0 % # 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[n0 % # ar, a], n→i(# ar), i0, i1 + 1)), 0 ≤ i0 + i1, n < i→n(i1), 0 < i1, # ar ≤ n0 ⊦ # ar = 0, ar[n0 % # ar] = a, # ar = 1, i1 = 0, i→n(i0) ≤ # ar ∧ i→n(i1) < # ar

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m * n = n * m], [CSIMPSEQ : ⊦ m0 * m * n = (m0 * m) * n], [CSIMPSEQ : ⊦ m0 * 1 = m0], [CSIMPSEQ : m2 ≠ 0 ⊦ ((* m2)) * m ≤ m + n0 ↔ (m2 - 1) * m ≤ n0], [CSIMPSEQ : ⊦ ¬ m < n ↔ n ≤ m], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + m = 2 * m])]]