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Proof step 19 from proof encode-contract (previous step)

# buf1 = n0 + ENCODED_ELEM_SIZE, # buf = n0 + ENCODED_ELEM_SIZE, subarray(buf1, ENCODED_ELEM_SIZE, n0) = subarray(buf, ENCODED_ELEM_SIZE, n0), subarray(buf1, 0, EB_PAGE_SIZE) = emptypage, is-encoded-nonempty(a, subarray(buf1, 0, ENCODED_ELEM_SIZE)), ENCODED_ELEM_SIZE ≤ EB_PAGE_SIZE, EB_PAGE_SIZE ≤ n0 + ENCODED_ELEM_SIZE ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ is-encoded-nonempty(a, buf) ↔ is-encoded(a, buf) ∧ ¬ isempty(buf)
Proof step 21:
# buf = n0 + ENCODED_ELEM_SIZE, # buf1 = n0 + ENCODED_ELEM_SIZE, subarray(buf1, 0, EB_PAGE_SIZE) = emptypage, subarray(buf1, ENCODED_ELEM_SIZE, n0) = subarray(buf, ENCODED_ELEM_SIZE, n0), is-encoded(a, subarray(buf1, 0, ENCODED_ELEM_SIZE)), EB_PAGE_SIZE ≤ n0 + ENCODED_ELEM_SIZE, ENCODED_ELEM_SIZE ≤ EB_PAGE_SIZE ⊦ isempty(subarray(buf1, 0, ENCODED_ELEM_SIZE))

Rule argument

spec: encoding-fixed-size-nonempty name: is-encoded-nonempty seq: ⊦ is-encoded-nonempty(a, buf) ↔ is-encoded(a, buf) ∧ ¬ isempty(buf) subst: [buf, a] → [subarray(buf1, 0, ENCODED_ELEM_SIZE), a] flags: <all paths>

Additional information

Used terms: subarray(buf1, 0, ENCODED_ELEM_SIZE), a