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Proof step 89 from proof push-corr (previous step)

buf .len < buf .size, inv(buf), 0 ≤ buf .len, 0 < buf .size ⊦ 0 ≤ (buf .first + buf .len) % buf .size ∧ (buf .first + buf .len) % buf .size < n→i(# buf .data)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 86:
⊦ 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 88:
buf .len < buf .size, buf .size = n→i(# buf .data) ∧ buf .size ≠ 0 ∧ 0 ≤ buf .first ∧ buf .first < buf .size ∧ 0 ≤ buf .len ∧ buf .len ≤ buf .size, 0 ≤ buf .len, 0 < buf .size ⊦ 0 ≤ (buf .first + buf .len) % buf .size ∧ (buf .first + buf .len) % buf .size < n→i(# buf .data)

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, 1)) dummy: () ]

Additional information

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