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Proof step 147 from proof encode (previous step)

# buf4 = # buf, # buf1 = # buf4, n2 = n1, subarray(buf4, ENCODED_NAT_SIZE, # buf - ENCODED_NAT_SIZE) = subarray(buf, ENCODED_NAT_SIZE, # buf - ENCODED_NAT_SIZE), vtbl0 = vtbl2, ENCODED_NAT_SIZE ≤ # buf, # vtbl2 * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) + ENCODED_NAT_SIZE ≤ # buf, err0 = ESUCCESS → is-encoded(# vtbl2, subarray(buf4, 0, ENCODED_NAT_SIZE)) ∧ n1 = ENCODED_NAT_SIZE, err = ESUCCESS → (∃ buf0, buf3, buf2, vtbl0. buf1 = buf0 + buf3 + buf2 ∧ vtbl2 = vtbl ∪ vtbl0 ∧ vtbl ⊥ vtbl0 ∧ # buf0 + # buf3 = n0 ∧ # buf2 ≥ # vtbl * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ∧ is-encoded(# vtbl2, buf0) ∧ is-encoded-rec(vtbl0, buf3)), err0 = ESUCCESS ∨ ⌊err0⌋ , err = ESUCCESS ∨ ⌊err⌋ ⊦ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # buf1 = # buf ∧ (err = ESUCCESS → is-encoded(vtbl0, buf1)), err = ESUCCESS ∧ vtbl ≠ ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 148:
# buf4 = # buf, # buf0 = ENCODED_NAT_SIZE, # buf2 = # vtbl0 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), ENCODED_NAT_SIZE + # buf2 + # buf3 = # buf, subarray(buf4, ENCODED_NAT_SIZE, # buf - ENCODED_NAT_SIZE) = subarray(buf, ENCODED_NAT_SIZE, # buf - ENCODED_NAT_SIZE), is-encoded(# vtbl0, buf0), is-encoded-rec(vtbl0, buf2), ENCODED_NAT_SIZE ≤ # buf, # buf2 + ENCODED_NAT_SIZE ≤ # buf, err0 = ESUCCESS → is-encoded(# vtbl0, subarray(buf4, 0, ENCODED_NAT_SIZE)) ∧ n1 = ENCODED_NAT_SIZE, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ is-encoded(vtbl0, buf0 + buf2 + buf3)

Rule argument

Additional information

Used simplifier rules: is-encoded-rec-size: ⊦ is-encoded-rec(vtbl, buf) → # buf = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE);%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ ∅ ⊥ vtbl; (s)% ⊦ 0 ≤ m; (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ 0 * n = 0; (s)% ⊦ # ∅ = 0; (s)% ⊦ ∅ ∪ vtbl = vtbl; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[encoding-nat-buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)%is-encoded-size: ⊦ is-encoded(n, buf) → # buf = ENCODED_NAT_SIZE; (forward) from specification encoding-fixed-size[encoding-nat]% ⊦ n ≥ m ↔ m ≤ n; (s)