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Proof step 9 from proof tolist-rec-inv (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ 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 8:
(i→n(buf .first) + n) % i→n(buf .size) ≤ i→n(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, # buf .data ≤ (i→n(buf .first) + n) % i→n(buf .size), # buf .data ≤ i→n(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, 1)) dummy: () ]

Additional information

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