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Proof step 36 from proof initial-ex-abstract-initial (previous step)

# 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])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 37:
# apebs + 1 = # pebs, pebs[# apebs] = mkpeb(buf, m, true), ubi-io-initial(pebs), ubi-io-initial(apebs), ∀ n0. n0 < # apebs → abs-peb(pebs[n0], apebs[n0]) ⊦ abs-peb(mkpeb(buf, m, true), mkpeb(empty, empty, mkbuf(LEB_SIZE), 0, true))

Rule argument

Additional information

Used simplifier rules: m < # apebs ⊦ apebs[m, apeb][m] = apeb; (s)% ⊦ m = n + 1 → ¬ m ≤ n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ # mkapebs(n) = n; (s)% ⊦ # copy(apebs, m, apebs0, m0, n) = # apebs0; (s)% ⊦ m ≤ m; (s)