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Proof step 15 from proof encode (previous step)

# buf1 = # buf, n0 = n, subarray(buf1, ENCODED_NAT_SIZE, # buf - ENCODED_NAT_SIZE) = subarray(buf, ENCODED_NAT_SIZE, # buf - ENCODED_NAT_SIZE), vtbl0 = vtbl, ENCODED_NAT_SIZE ≤ # buf, # vtbl * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) + ENCODED_NAT_SIZE ≤ # buf, err = ESUCCESS → is-encoded(# vtbl, subarray(buf1, 0, ENCODED_NAT_SIZE)) ∧ n = ENCODED_NAT_SIZE, err = ESUCCESS ∨ ⌊err⌋ ⊦ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # buf1 = # buf1 ∧ ( err = ESUCCESS → (∃ buf0, buf3, buf2, vtbl0. buf1 = buf0 + buf3 + buf2 ∧ vtbl = vtbl ∪ vtbl0 ∧ vtbl ⊥ vtbl0 ∧ # buf0 + # buf3 = n0 ∧ # buf2 ≥ # vtbl * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ∧ is-encoded(# vtbl, buf0) ∧ is-encoded-rec(vtbl0, buf3)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
# buf1 = # buf, subarray(buf1, ENCODED_NAT_SIZE, # buf - ENCODED_NAT_SIZE) = subarray(buf, ENCODED_NAT_SIZE, # buf - ENCODED_NAT_SIZE), is-encoded(# vtbl, subarray(buf1, 0, ENCODED_NAT_SIZE)), ENCODED_NAT_SIZE ≤ # buf, # vtbl * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) + 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)

Rule argument

Additional information

Used simplifier rules: ⊦ # subarray(buf, m, n) = n; (s)%is-encoded-size: ⊦ is-encoded(n, buf) → # buf = ENCODED_NAT_SIZE; (forward) from specification encoding-fixed-size[encoding-nat]% ⊦ n ≥ m ↔ m ≤ n; (s)