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Proof step 5 from proof clear-corr (previous step)

inv(mk(ar, i, i0, i1)) ⊦ i = n→i(# ar) ∧ # ar ≠ 0 ∧ 0 ≤ i0 ∧ i0 < n→i(# ar)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ 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, i1)] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 0)) 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 : ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ n→i(n) = 0 ↔ n = 0], [CSIMPSEQ : ⊦ 0 ≤ n→i(n)], [CSIMPSEQ : 0 ≤ i ⊦ ((* i)) < n→i(n) ↔ i→n(i) < n], [CSIMPSEQ : ⊦ 0 < m ↔ m ≠ 0])], [EXTRATERMS : (mk(ar, i, i0, i1))]]