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Proof step 28 from proof initial-ex-abstract-initial (previous step)

m0 + 1 = # pebs, pebs[m0] = mkpeb(buf, m, true), abs(subarray(pebs, 0, m0), apebs), ubi-io-initial(apebs), ubi-io-initial(pebs) ⊦ abs(pebs, copy(apebs, 0, mkapebs(m0 + 1), 0, m0)[m0, mkpeb(empty, empty, mkbuf(LEB_SIZE), 0, true)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 29:
⊦ abs(pebs, apebs) ↔ # pebs = # apebs ∧ (∀ n. n < # pebs → abs-peb(pebs[n], apebs[n]))
Proof step 30:
m0 + 1 = # pebs, pebs[m0] = mkpeb(buf, m, true), abs(subarray(pebs, 0, m0), apebs), ubi-io-initial(pebs), ubi-io-initial(apebs) ⊦ # pebs = # copy(apebs, 0, mkapebs(m0 + 1), 0, m0)[m0, mkpeb(empty, empty, mkbuf(LEB_SIZE), 0, true)] ∧ (∀ n. n < # pebs → abs-peb(pebs[n], copy(apebs, 0, mkapebs(m0 + 1), 0, m0)[m0, mkpeb(empty, empty, mkbuf(LEB_SIZE), 0, true)][n]))

Rule argument

spec: ubi-io-abs name: abs seq: ⊦ abs(pebs, apebs) ↔ # pebs = # apebs ∧ (∀ n. n < # pebs → abs-peb(pebs[n], apebs[n])) subst: [apebs, pebs] → [copy(apebs, 0, mkapebs(m0 + 1), 0, m0) [m0, mkpeb(empty, empty, mkbuf(LEB_SIZE), 0, true) ], pebs] flags: <all paths>

Additional information

Used terms: copy(apebs, 0, mkapebs(m0 + 1), 0, m0) [m0, mkpeb(empty, empty, mkbuf(LEB_SIZE), 0, true) ], pebs