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Proof step 16 from proof encode (previous step)

# 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)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 17:
# 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)

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [# buf, ENCODED_NAT_SIZE, n]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: # buf, ENCODED_NAT_SIZE, n