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Proof step 52 from proof push-corr (previous step)

(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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 51:
i→n(i0) + i→n(i1) = n0 + # ar, n0 % # 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

[x0lemmaarg: spec-name: nat instance-name: lemma-name: elim-sub antecedent: n ≤ m succedent: n0 = m - n ↔ m = n0 + n substlist: [m, n, n0] → [i→n(i0) + i→n(i1), # ar, n0] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : n ≤ m ⊦ n0 = m - n ↔ m = n0 + n])], [EXTRATERMS : (i→n(i0) + i→n(i1), # ar, n0)]]