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Proof step 34 from proof initial-ex-abstract-initial (previous step)

# apebs + 1 = # pebs, pebs[# apebs] = mkpeb(buf, m, true), ubi-io-initial(pebs), ubi-io-initial(apebs), n ≤ # apebs, ∀ n0. n0 < # apebs → abs-peb(pebs[n0], apebs[n0]) ⊦ abs-peb(pebs[n], copy(apebs, 0, mkapebs(# pebs), 0, # apebs)[# apebs, mkpeb(empty, empty, mkbuf(LEB_SIZE), 0, true)][n])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 35:
⊦ m ≠ n → apebs[n, apeb][m] = apebs[m]
Proof step 36:
# apebs + 1 = # pebs, pebs[# apebs] = mkpeb(buf, m, true), n = # apebs, ubi-io-initial(apebs), ubi-io-initial(pebs), n ≤ # apebs, ∀ n0. n0 < # apebs → abs-peb(pebs[n0], apebs[n0]) ⊦ abs-peb(pebs[n], copy(apebs, 0, mkapebs(# pebs), 0, # apebs)[# apebs, mkpeb(empty, empty, mkbuf(LEB_SIZE), 0, true)][n])
Proof step 39:
# apebs + 1 = # pebs, pebs[# apebs] = mkpeb(buf, m, true), ubi-io-initial(apebs), ubi-io-initial(pebs), n ≤ # apebs, ∀ n0. n0 < # apebs → abs-peb(pebs[n0], apebs[n0]) ⊦ n = # apebs, abs-peb(pebs[n], copy(apebs, 0, mkapebs(# pebs), 0, # apebs)[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), # apebs, copy(apebs, 0, mkapebs(# pebs), 0, # apebs)] flags: <all paths>

Additional information

Used terms: n, mkpeb(empty, empty, mkbuf(LEB_SIZE), 0, true), # apebs, copy(apebs, 0, mkapebs(# pebs), 0, # apebs)