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Proof step 60 from proof decode (previous step)

# 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 + ENCODED_VOLID_SIZE = n0 + # buf4, 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, # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ≤ # buf4 + # buf0 + # buf3, ENCODED_NAT_SIZE + (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * (m0 + # vtbl) ≤ # buf4 + # buf0 + # buf3, # buf2 ≤ n0, n0 + # buf0 ≤ # buf2 + #(buf1 + buf0 + 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(buf1 + buf0 + buf3, n0 - # buf2, # buf0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 61:
# 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 + ENCODED_VOLID_SIZE = n0 + # buf4, 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, n0 ≤ ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE + # buf3, # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ≤ # buf4 + # buf0 + # buf3, ENCODED_NAT_SIZE + (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * (m0 + # vtbl) ≤ # buf4 + # buf0 + # buf3, ENCODED_VOLID_SIZE ≤ n0, 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(buf1 + buf0 + buf3, n0 - ENCODED_VOLID_SIZE, # buf0))

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m + n; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[encoding-nat-buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)