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Proof step 17 from proof pop-corr (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ x0 = x1 ↔ # x0 = # x1 ∧ (∀ n. n < # x0 → x0[n] = x1[n])
Proof step 16:
a ' + x = tolist(mk(ar, i, i0, n→i(# x) + 1), 1 + # x), 0 ≤ i0, inv(mk(ar, i, (i0 + 1) % i, n→i(# x))), inv(mk(ar, i, i0, n→i(# x) + 1)), i0 < n→i(# ar) ⊦ # x = # tolist(mk(ar, i, (i0 + 1) % i, n→i(# x)), # x) ∧ (∀ n. n < # x → x[n] = (tolist(mk(ar, i, (i0 + 1) % i, n→i(# x)), # x)[n])), # ar = 0

Rule argument

[x0lemmaarg: spec-name: list-del instance-name: queue lemma-name: extension antecedent: succedent: x0 = x1 ↔ # x0 = # x1 ∧ (∀ n. n < # x0 → x0[n] = x1[n]) substlist: [x1, x0] → [tolist(mk(ar, i, (i0 + 1) % i, n→i(# x)), # x), x] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (tolist(mk(ar, i, (i0 + 1) % i, n→i(# x)), # x), x)]]