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Proof step 45 from proof encode (previous step)

# buf5 = # buf4, # buf2 = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf0 = ENCODED_NAT_SIZE, # buf4 = (# buf2 + ENCODED_VOLID_SIZE + n2) + ENCODED_NAT_SIZE, # buf = # buf4, # buf3 = ENCODED_VOLID_SIZE + n2, n = ENCODED_VOLID_SIZE, subarray(buf5, 0, ENCODED_NAT_SIZE + # buf2) = buf0 + buf2, subarray(buf5, ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE, n2) = subarray(buf3, ENCODED_VOLID_SIZE, n2), subarray(buf4, ENCODED_NAT_SIZE, # buf2 + ENCODED_VOLID_SIZE + n2) = subarray(buf, ENCODED_NAT_SIZE, # buf2 + ENCODED_VOLID_SIZE + n2), vtbl1 ≠ ∅, is-encoded(v, subarray(buf5, ENCODED_NAT_SIZE + # buf2, ENCODED_VOLID_SIZE)), is-encoded(#(vtbl1 ∪ vtbl), buf0), is-encoded-rec(vtbl, buf2), v ∈ vtbl1, ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ≤ # buf4, # vtbl1 * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ ENCODED_VOLID_SIZE + n2, #(vtbl1 ∪ vtbl) * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf2 + ENCODED_VOLID_SIZE + n2, vtbl1 ⊥ vtbl, ¬ v ∈ vtbl, err0 = ESUCCESS → is-encoded(#(vtbl1 ∪ vtbl), subarray(buf4, 0, ENCODED_NAT_SIZE)) ∧ n1 = ENCODED_NAT_SIZE, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ ⟪encode_nat#(vtbl1[v], (ENCODED_NAT_SIZE + # buf2) + ENCODED_VOLID_SIZE; buf5, n; err); n0 := ((ENCODED_NAT_SIZE + # buf2) + ENCODED_VOLID_SIZE) + n; vtbl0 := vtbl1 -- v⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # buf5 = # buf4 ∧ ( err = ESUCCESS → (∃ buf0, buf2, buf, vtbl3. buf5 = buf0 + buf2 + buf ∧ vtbl1 ∪ vtbl = vtbl0 ∪ vtbl3 ∧ vtbl0 ⊥ vtbl3 ∧ # buf0 + # buf2 = n0 ∧ # vtbl0 * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf ∧ is-encoded(#(vtbl0 ∪ vtbl3), buf0) ∧ is-encoded-rec(vtbl3, buf2))) ∧ # vtbl0 < # vtbl1)

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: encoding, inst: encoding-nat name: encode-contract seq: n1 + encoding-size(n) ≤ # buf, buf0 = buf ⊦ ⟪encode_nat#(n, n1; buf, n0; err)⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # buf = # buf0 ∧ subarray(buf, 0, n1) = subarray(buf0, 0, n1) ∧ subarray (buf, n1 + encoding-size(n), # buf - n1 + encoding-size(n)) = subarray (buf0, n1 + encoding-size(n), # buf - n1 + encoding-size(n)) ∧ ( err = ESUCCESS → is-encoded(n, subarray(buf, n1, encoding-size(n))) ∧ n0 = encoding-size(n))) subst: [n1, n, n0, buf, err, buf0] → [(ENCODED_NAT_SIZE + # buf2) + ENCODED_VOLID_SIZE, vtbl1[v], n, buf5, err, buf5] flags: <all paths>

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