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Proof step 150 from proof encode (previous step)

# buf = # buf4, # buf4 = (# buf2 + # buf3) + ENCODED_NAT_SIZE, # buf0 = ENCODED_NAT_SIZE, # buf2 = # vtbl0 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), subarray(buf4, ENCODED_NAT_SIZE, # buf2 + # buf3) = subarray(buf, ENCODED_NAT_SIZE, # buf2 + # buf3), is-encoded(# vtbl0, buf0), is-encoded-rec(vtbl0, buf2), err0 = ESUCCESS → is-encoded(# vtbl0, subarray(buf4, 0, ENCODED_NAT_SIZE)) ∧ n1 = ENCODED_NAT_SIZE, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ is-encoded(vtbl0, buf0 + buf2 + buf3)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 151:
⊦ is-encoded(vtbl, buf) ↔ (∃ buf0, buf1, buf2. buf = buf0 + buf1 + buf2 ∧ is-encoded(# vtbl, buf0) ∧ is-encoded-rec(vtbl, buf1))
Proof step 152:
# buf2 = # vtbl0 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf0 = ENCODED_NAT_SIZE, # buf4 = (# buf2 + # buf3) + ENCODED_NAT_SIZE, # buf = # buf4, subarray(buf4, ENCODED_NAT_SIZE, # buf2 + # buf3) = subarray(buf, ENCODED_NAT_SIZE, # buf2 + # buf3), is-encoded(# vtbl0, buf0), is-encoded-rec(vtbl0, buf2), err0 = ESUCCESS → is-encoded(# vtbl0, subarray(buf4, 0, ENCODED_NAT_SIZE)) ∧ n1 = ENCODED_NAT_SIZE, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ ∃ buf4, buf1, buf5. buf0 + buf2 + buf3 = buf4 + buf1 + buf5 ∧ is-encoded(# vtbl0, buf4) ∧ is-encoded-rec(vtbl0, buf1)

Rule argument

spec: <toplevel> name: is-encoded seq: ⊦ is-encoded(vtbl, buf) ↔ (∃ buf0, buf1, buf2. buf = buf0 + buf1 + buf2 ∧ is-encoded(# vtbl, buf0) ∧ is-encoded-rec(vtbl, buf1)) subst: [buf, vtbl] → [buf0 + buf2 + buf3, vtbl0] flags: <all paths>

Additional information

Used terms: buf0 + buf2 + buf3, vtbl0