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Proof step 68 from proof decode (previous step)

# buf4 = ENCODED_NAT_SIZE + # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf0 = m0 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # vtbl1 = m0 + 1, # buf2 = ENCODED_VOLID_SIZE, # buf1 = ENCODED_NAT_SIZE, 2 * ENCODED_NAT_SIZE + (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * # vtbl = n1 + # buf4, is-encoded((m0 + 1) + # vtbl, subarray(buf4, 0, ENCODED_NAT_SIZE)), is-encoded(vtbl0, buf4 + (buf2 + buf1 + buf0) + buf3), is-encoded(vtbl1[v], buf1), is-encoded(v, buf2), is-encoded-rec(vtbl, subarray(buf4, ENCODED_NAT_SIZE, # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE))), is-encoded-rec(vtbl1 -- v, buf0), v ∈ vtbl1, n1 ≤ ENCODED_NAT_SIZE + # buf3, ENCODED_NAT_SIZE + (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * (m0 + # vtbl) ≤ # buf4 + # buf0 + # buf3, # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ≤ # buf4 + # buf0 + # buf3, ENCODED_NAT_SIZE ≤ n1, vtbl ⊥ vtbl1, err0 = ESUCCESS → n3 = ENCODED_NAT_SIZE, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ vtbl1 = ∅, v ∈ vtbl, is-encoded-rec (vtbl[v, vtbl1[v]], subarray (buf4 + (buf2 + buf1 + buf0) + buf3, ENCODED_NAT_SIZE, (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * # vtbl + ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE)) ∧ is-encoded-rec(vtbl1 -- v, subarray(buf0 + buf3, n1 - ENCODED_NAT_SIZE, # buf0))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 69:
# buf1 = ENCODED_NAT_SIZE, # buf2 = ENCODED_VOLID_SIZE, # vtbl1 = m0 + 1, # buf0 = m0 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf4 = ENCODED_NAT_SIZE + # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), 2 * ENCODED_NAT_SIZE + (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * # vtbl = n1 + # buf4, n1 = n0 + ENCODED_NAT_SIZE, is-encoded(v, buf2), is-encoded(vtbl1[v], buf1), is-encoded(vtbl0, buf4 + (buf2 + buf1 + buf0) + buf3), is-encoded((m0 + 1) + # vtbl, subarray(buf4, 0, ENCODED_NAT_SIZE)), is-encoded-rec(vtbl1 -- v, buf0), is-encoded-rec(vtbl, subarray(buf4, ENCODED_NAT_SIZE, # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE))), v ∈ vtbl1, ENCODED_NAT_SIZE ≤ n1, # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ≤ # buf4 + # buf0 + # buf3, ENCODED_NAT_SIZE + (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * (m0 + # vtbl) ≤ # buf4 + # buf0 + # buf3, n1 ≤ ENCODED_NAT_SIZE + # buf3, vtbl ⊥ vtbl1, err0 = ESUCCESS → n3 = ENCODED_NAT_SIZE, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ vtbl1 = ∅, v ∈ vtbl, is-encoded-rec (vtbl[v, vtbl1[v]], subarray (buf4 + (buf2 + buf1 + buf0) + buf3, ENCODED_NAT_SIZE, (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * # vtbl + ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE)) ∧ is-encoded-rec(vtbl1 -- v, subarray(buf0 + buf3, n0, # buf0))

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [n1, ENCODED_NAT_SIZE, n]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n1, ENCODED_NAT_SIZE, n