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Proof step 15 from proof pop-corr (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ inv(buf) ∧ m < n → (x = tolist(buf, n) ↔ x = tolist(buf, n) ∧ x[m] = (buf .data)[(i→n(buf .first) + m) % i→n(buf .size)])
Proof step 14:
inv(mk(ar, i, i0, n→i(# x) + 1)) ∧ n + 1 < 1 + # x, a ' + x = tolist(mk(ar, i, i0, n→i(# x) + 1), 1 + # x) ∧ (a ' + x)[n + 1] = (mk(ar, i, i0, n→i(# x) + 1) .data)[(i→n(mk(ar, i, i0, n→i(# x) + 1) .first) + n + 1) % i→n(mk(ar, i, i0, n→i(# x) + 1) .size)], n < # 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 ⊦ x[n] = ar[(i→n((i0 + 1) % i) + n) % i→n(i)], # ar = 0, x = []

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: tolist-ext-one antecedent: succedent: inv(buf) ∧ m < n → ( x = tolist(buf, n) ↔ x = tolist(buf, n) ∧ x[m] = (buf .data)[(i→n(buf .first) + m) % i→n(buf .size)]) substlist: [m, n, buf, x] → [n + 1, 1 + # x, mk(ar, i, i0, n→i(# x) + 1), a ' + x] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ m + n < m + n0 ↔ n < n0], [CSIMPSEQ : ⊦ ¬ m < n ↔ n ≤ m], [CSIMPSEQ : ⊦ m < n → (n ≤ m ↔ false)], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m])], [EXTRATERMS : (n + 1, 1 + # x, mk(ar, i, i0, n→i(# x) + 1), a ' + x)]]