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Proof step 30 from proof pop-corr (previous step)

a ' + x = tolist(mk(ar, i, i0, n→i(# x) + 1), 1 + # x), i0 < n→i(# ar), inv(mk(ar, i, i0, n→i(# x) + 1)), inv(mk(ar, i, (i0 + 1) % i, n→i(# x))), 0 ≤ i0, ¬ abs(mk(ar, i, (i0 + 1) % i, n→i(# x)), x) ∨ a ≠ ar[i→n(i0)] ⊦ # ar = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ abs(buf, x) ↔ buf .len = n→i(# x) ∧ x = tolist(buf, i→n(buf .len))
Proof step 29:
a ' + x = tolist(mk(ar, i, i0, n→i(# x) + 1), 1 + # x), i0 < n→i(# ar), inv(mk(ar, i, i0, n→i(# x) + 1)), inv(mk(ar, i, (i0 + 1) % i, n→i(# x))), 0 ≤ i0, ¬ (mk(ar, i, (i0 + 1) % i, n→i(# x)) .len = n→i(# x) ∧ x = tolist(mk(ar, i, (i0 + 1) % i, n→i(# x)), i→n(mk(ar, i, (i0 + 1) % i, n→i(# x)) .len))) ∨ a ≠ ar[i→n(i0)] ⊦ # ar = 0

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: abs antecedent: succedent: abs(buf, x) ↔ buf .len = n→i(# x) ∧ x = tolist(buf, i→n(buf .len)) substlist: [x, buf] → [x, mk(ar, i, (i0 + 1) % i, n→i(# x))] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 5, 1, 0, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (x, mk(ar, i, (i0 + 1) % i, n→i(# x)))]]