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Proof step 20 from proof decode (previous step)

# vtbl1 = m0 + 1, is-encoded(# vtbl1 + # vtbl, subarray(buf, 0, ENCODED_NAT_SIZE)), is-encoded(vtbl0, buf), is-encoded-rec (vtbl1, subarray(buf, ENCODED_NAT_SIZE + # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # vtbl1 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE))), is-encoded-rec(vtbl, subarray(buf, ENCODED_NAT_SIZE, # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE))), ENCODED_NAT_SIZE + (# vtbl1 + # vtbl) * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ≤ # buf, vtbl ⊥ vtbl1, err0 = ESUCCESS → ENCODED_NAT_SIZE ≤ # buf ∧ n3 = ENCODED_NAT_SIZE, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ ⟪decode_volid#(ENCODED_NAT_SIZE + # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), buf; v, n; err); n0 := ENCODED_NAT_SIZE + # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE); n5 := # vtbl1 + # vtbl; if err = ESUCCESS then {n0 := n0 + n; decode_nat#(n0, buf; m, n; err); if err = ESUCCESS then {n0 := n0 + n; vtbl[v] := m}}; n1 := m0⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → (∃ vtbl2. vtbl ⊥ vtbl2 ∧ # vtbl2 + # vtbl = n5 ∧ # vtbl2 = n1 ∧ ENCODED_NAT_SIZE + (# vtbl2 + # vtbl) * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ≤ # buf ∧ n0 = ENCODED_NAT_SIZE + # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ∧ is-encoded(# vtbl2 + # vtbl, subarray(buf, 0, ENCODED_NAT_SIZE)) ∧ is-encoded-rec(vtbl, subarray(buf, ENCODED_NAT_SIZE, # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE))) ∧ is-encoded-rec (vtbl2, subarray (buf, ENCODED_NAT_SIZE + # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # vtbl2 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE))))) ∧ n1 < # vtbl1), # vtbl1 = 0, vtbl1 = ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
# vtbl1 = m0 + 1, vtbl1 ≠ ∅, is-encoded(vtbl0, buf), is-encoded((m0 + 1) + # vtbl, subarray(buf, 0, ENCODED_NAT_SIZE)), is-encoded-rec(vtbl, subarray(buf, ENCODED_NAT_SIZE, # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE))), is-encoded-rec (vtbl1, subarray (buf, ENCODED_NAT_SIZE + # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * m0 + ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE)), 2 * ENCODED_NAT_SIZE + (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * (m0 + # vtbl) + ENCODED_VOLID_SIZE ≤ # buf, vtbl ⊥ vtbl1, err0 = ESUCCESS → ENCODED_NAT_SIZE ≤ # buf ∧ n3 = ENCODED_NAT_SIZE, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ ⟪decode_volid#(ENCODED_NAT_SIZE + # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), buf; v, n; err); n0 := ENCODED_NAT_SIZE + # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE); n5 := (m0 + 1) + # vtbl; if err = ESUCCESS then {n0 := n0 + n; decode_nat#(n0, buf; m, n; err); if err = ESUCCESS then {n0 := n0 + n; vtbl[v] := m}}; n1 := m0⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → (∃ vtbl2. vtbl ⊥ vtbl2 ∧ # vtbl2 + # vtbl = n5 ∧ # vtbl2 = n1 ∧ ENCODED_NAT_SIZE + (# vtbl2 + # vtbl) * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ≤ # buf ∧ n0 = ENCODED_NAT_SIZE + # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ∧ is-encoded(# vtbl2 + # vtbl, subarray(buf, 0, ENCODED_NAT_SIZE)) ∧ is-encoded-rec(vtbl, subarray(buf, ENCODED_NAT_SIZE, # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE))) ∧ is-encoded-rec (vtbl2, subarray (buf, ENCODED_NAT_SIZE + # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # vtbl2 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE))))) ∧ n1 < # vtbl1)

Rule argument

Additional information

Used simplifier rules: is-encoded-rec-size: ⊦ is-encoded-rec(vtbl, buf) → # buf = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE);% ⊦ m + m = 2 * m; (s)% ⊦ m * n + n = m1 * n ↔ m + 1 = m1 ∨ n = 0; (s)% ⊦ # subarray(buf, m, n) = n; (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m * (n + 1) = m * n + m; (s)% ⊦ # vtbl = 0 ↔ vtbl = ∅; (s)