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Proof step 36 from proof push-corr (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 35:
i→n(i0) + n = n0 + # ar, i→n(i0) + i→n(i1) = n0 % # ar + # ar, i→n(i0) + 1 < i→n(i1), # ar + 1 < i→n(i1), i→n(i0) + 1 < n, # ar < n, n0 % # ar < n0, 0 ≤ (i0 + i1) % n→i(# ar), 0 ≤ i0, i1 ≤ n→i(# ar), i→n(i0) < # 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, n0 % # ar < n0 + # ar, # ar ≤ n0, i→n(i0) < n0, i→n(i0) < n, # ar < i→n(i1), i0 < i1, i0 < n→i(# ar), 2 + i→n(i0) < i→n(i1) ⊦ ar[n0 % # ar] = a, # ar = 1, i1 = 0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ n < n0 ∧ n0 < n1 → n < n1], [CSIMPSEQ : ⊦ m +1 = m + 1], [CSIMPFORWARD : ⊦ m < n ∧ n < n0 → m +1 < n0], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m < n → m ≤ n])]]