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Proof step 43 from proof push-corr (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 42:
i→n(i0) + i→n(i1) = n0 % # ar + # ar, i→n(i0) + n = n0 + # ar, n0 % # ar < n0 + # ar, n0 % # ar < # 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, n0 % # ar < n0 ⊦ i1 = 0, # ar = 1, ar[n0 % # ar] = a

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m < n → n ≠ 0], [CSIMPFORWARD : ⊦ m < n → n ≠ 0], [CSIMPFORWARD : ⊦ m < n ∧ n ≤ n0 → m < n0], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ ¬ m < n ↔ n ≤ m])]]