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Proof step 51 from proof pop-corr (previous step)

a ' + x = tolist(buf, i→n(buf .len)), buf .len = 1 + n→i(# x), 0 ≤ buf .first, buf .first < n→i(# buf .data), inv(buf), ¬ inv(buf .first:= ((buf .first + 1) % buf .size) .len:= (buf .len - 1)) ∨ ¬ abs(buf .first:= ((buf .first + 1) % buf .size) .len:= (buf .len - 1), x) ∨ a ≠ (buf .data)[i→n(buf .first)] ⊦ # buf .data = 0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 50:
buf .len = i0 + 1, a ' + x = tolist(buf, i→n(buf .len)), buf .len = 1 + n→i(# x), 0 ≤ buf .first, buf .first < n→i(# buf .data), inv(buf), ¬ inv(buf .first:= ((buf .first + 1) % buf .size) .len:= i0) ∨ ¬ abs(buf .first:= ((buf .first + 1) % buf .size) .len:= i0, x) ∨ a ≠ (buf .data)[i→n(buf .first)] ⊦ # buf .data = 0

Rule argument

[x0lemmaarg: spec-name: int-abs instance-name: lemma-name: elim-sub antecedent: succedent: i0 = i - j ↔ i = i0 + j substlist: [i, j, i0] → [buf .len, 1, i] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ i0 = i - j ↔ i = i0 + j])], [EXTRATERMS : (buf .len, 1, i)]]