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Proof step 47 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), n ≤ m0 ⊦ ubi-io-peb-initial(copy(apebs, 0, mkapebs(m0 + 1), 0, m0)[m0, mkpeb(empty, empty, mkbuf(LEB_SIZE), 0, true)][n])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 48:
⊦ m ≠ n → apebs[n, apeb][m] = apebs[m]
Proof step 49:
m0 + 1 = # pebs, pebs[m0] = mkpeb(buf, m, true), n = m0, abs(subarray(pebs, 0, m0), apebs), ubi-io-initial(pebs), ubi-io-initial(apebs), n ≤ m0 ⊦ ubi-io-peb-initial(copy(apebs, 0, mkapebs(m0 + 1), 0, m0)[m0, mkpeb(empty, empty, mkbuf(LEB_SIZE), 0, true)][n])
Proof step 52:
m0 + 1 = # pebs, pebs[m0] = mkpeb(buf, m, true), abs(subarray(pebs, 0, m0), apebs), ubi-io-initial(pebs), ubi-io-initial(apebs), n ≤ m0 ⊦ n = m0, ubi-io-peb-initial(copy(apebs, 0, mkapebs(m0 + 1), 0, m0)[n])

Rule argument

spec: array, inst: apebs name: Put-other seq: ⊦ m ≠ n → apebs[n, apeb][m] = apebs[m] subst: [m, apeb, n, apebs] → [n, mkpeb(empty, empty, mkbuf(LEB_SIZE), 0, true), m0, copy(apebs, 0, mkapebs(m0 + 1), 0, m0)] flags: <all paths>

Additional information

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