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Proof step 17 from proof encode (previous step)

# buf1 = # buf, # buf = 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) + ENCODED_NAT_SIZE ≤ # buf, ENCODED_NAT_SIZE ≤ # buf ⊦ ∃ buf0, buf2, buf3, vtbl0. buf1 = buf0 + buf2 + buf3 ∧ vtbl = vtbl ∪ vtbl0 ∧ vtbl ⊥ vtbl0 ∧ # buf0 + # buf2 = ENCODED_NAT_SIZE ∧ # vtbl * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf3 ∧ is-encoded(# vtbl, buf0) ∧ is-encoded-rec(vtbl0, buf2)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
# buf1 = n0 + ENCODED_NAT_SIZE, # buf = 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 ⊦ ∃ buf0, buf2, buf3, vtbl0. buf1 = buf0 + buf2 + buf3 ∧ vtbl = vtbl ∪ vtbl0 ∧ vtbl ⊥ vtbl0 ∧ # buf0 + # buf2 = ENCODED_NAT_SIZE ∧ # vtbl * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf3 ∧ is-encoded(# vtbl, buf0) ∧ is-encoded-rec(vtbl0, buf2)

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ 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 ≤ m + n0 ↔ n ≤ n0; (s)