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Proof step 19 from proof encode (previous step)

# buf = n0 + ENCODED_NAT_SIZE, # buf1 = n0 + ENCODED_NAT_SIZE, subarray(buf1, ENCODED_NAT_SIZE, n0) = subarray(buf, ENCODED_NAT_SIZE, n0), is-encoded(# vtbl, subarray(buf1, 0, ENCODED_NAT_SIZE)), # vtbl * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ n0 ⊦ buf1 = subarray(buf1, 0, ENCODED_NAT_SIZE) + mkbuf(0) + subarray(buf1, ENCODED_NAT_SIZE, # buf1 - ENCODED_NAT_SIZE) ∧ vtbl = vtbl ∪ ∅ ∧ vtbl ⊥ ∅ ∧ # subarray(buf1, 0, ENCODED_NAT_SIZE) + # mkbuf(0) = ENCODED_NAT_SIZE ∧ # vtbl * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # subarray(buf1, ENCODED_NAT_SIZE, # buf1 - ENCODED_NAT_SIZE) ∧ is-encoded(# vtbl, subarray(buf1, 0, ENCODED_NAT_SIZE)) ∧ is-encoded-rec(∅, mkbuf(0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
# buf = n0 + ENCODED_NAT_SIZE, # buf1 = n0 + ENCODED_NAT_SIZE, subarray(buf1, ENCODED_NAT_SIZE, n0) = subarray(buf, ENCODED_NAT_SIZE, n0), is-encoded(# vtbl, subarray(buf1, 0, ENCODED_NAT_SIZE)), # vtbl * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ n0 ⊦ buf1 = subarray(buf1, 0, ENCODED_NAT_SIZE) + subarray(buf, ENCODED_NAT_SIZE, n0)

Rule argument

Additional information

Used simplifier rules: is-encoded-base: ⊦ is-encoded-rec(∅, buf) ↔ # buf = 0;% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m + n - m = n; (s)% ⊦ is-encoded(n, buf) → (is-encoded(n0, buf) ↔ n = n0); (s)%n0 ≤ n ⊦ m ≤ n - n0 ↔ m + n0 ≤ n; (s)% ⊦ ¬ m + n < m; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ # mkbuf(n) = n; (s)% ⊦ # subarray(buf, m, n) = n; (s)% ⊦ vtbl ⊥ ∅; (s)% ⊦ vtbl ∪ ∅ = vtbl; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[encoding-nat-buffer]% ⊦ mkbuf(0) + buf = buf; (s)