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Proof step 45 from proof pop-corr (previous step)

buf .len = n→i(# x) + 1, a ' + x = tolist(buf, 1 + # x), 0 ≤ buf .first, buf .first < n→i(# buf .data), inv(buf) ⊦ # buf .data = 0, buf .size = n→i(# buf .data) ∧ buf .size ≠ 0 ∧ 0 ≤ (buf .first + 1) % buf .size ∧ (buf .first + 1) % buf .size < buf .size ∧ n→i(# x) ≤ buf .size

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 35:
⊦ inv(buf) ↔ buf .size = n→i(# buf .data) ∧ buf .size ≠ 0 ∧ 0 ≤ buf .first ∧ buf .first < buf .size ∧ 0 ≤ buf .len ∧ buf .len ≤ buf .size
Proof step 44:
buf .len = n→i(# x) + 1, a ' + x = tolist(buf, 1 + # x), 0 ≤ buf .first, buf .first < n→i(# buf .data), buf .size = n→i(# buf .data) ∧ buf .size ≠ 0 ∧ 0 ≤ buf .first ∧ buf .first < buf .size ∧ 0 ≤ buf .len ∧ buf .len ≤ buf .size ⊦ # buf .data = 0, buf .size = n→i(# buf .data) ∧ buf .size ≠ 0 ∧ 0 ≤ (buf .first + 1) % buf .size ∧ (buf .first + 1) % buf .size < buf .size ∧ n→i(# x) ≤ buf .size

Rule argument

[x0lemmaarg: spec-name: ring-buffer-inv instance-name: lemma-name: inv antecedent: succedent: inv(buf) ↔ buf .size = n→i(# buf .data) ∧ buf .size ≠ 0 ∧ 0 ≤ buf .first ∧ buf .first < buf .size ∧ 0 ≤ buf .len ∧ buf .len ≤ buf .size substlist: [buf] → [buf] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 4)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (buf)]]