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Proof step 22 from proof pop-corr (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ 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

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] → [mk(ar, i, (i0 + 1) % i, n→i(# x))] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 3)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ mk(ar, i, i0, i1) .size = i], [CSIMPSEQ : ⊦ mk(ar, i, i0, i1) .data = ar], [CSIMPSEQ : ⊦ mk(ar, i, i0, i1) .first = i0], [CSIMPSEQ : ⊦ mk(ar, i, i0, i1) .len = i1], [CSIMPSEQ : ⊦ 0 ≤ n→i(n)], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPSEQ : ⊦ i→n(n→i(n)) = n], [CSIMPSEQ : ⊦ n→i(n) = 0 ↔ n = 0], [CSIMPSEQ : 0 ≤ i ⊦ ((* i)) < n→i(n) ↔ i→n(i) < n], [CSIMPSEQ : ⊦ 0 < m ↔ m ≠ 0], [CSIMPSEQ : ⊦ n→i(m) ≤ n→i(n) ↔ m ≤ n], [CSIMPSEQ : ⊦ abs(n→i(n)) = n→i(n)], [CSIMPSEQ : ⊦ n→i(m) < n→i(n) ↔ m < n], [CSIMPSEQ : ⊦ ¬ n < n])], [EXTRATERMS : (mk(ar, i, (i0 + 1) % i, n→i(# x)))]]