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Proof step 24 from proof encode (previous step)

# buf1 = # buf4, # buf4 = # buf, err = ESUCCESS, n2 = n1, subarray(buf4, ENCODED_NAT_SIZE, # buf - ENCODED_NAT_SIZE) = subarray(buf, ENCODED_NAT_SIZE, # buf - ENCODED_NAT_SIZE), vtbl = vtbl1, vtbl0 = vtbl2, v ∈ vtbl, # vtbl2 * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) + ENCODED_NAT_SIZE ≤ # buf, ENCODED_NAT_SIZE ≤ # buf, 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 → is-encoded(# vtbl2, subarray(buf4, 0, ENCODED_NAT_SIZE)) ∧ n1 = ENCODED_NAT_SIZE, err = ESUCCESS ∨ ⌊err⌋ , err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ ⟪encode_volid#(v, n0; buf1, n; err); if err = ESUCCESS then {n0 := n0 + n; encode_nat#(vtbl[v], n0; buf1, n; err); n0 := n0 + n}; vtbl := vtbl -- v⟫ ( ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # buf1 = # buf4 ∧ ( 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)))) ∧ # vtbl < # vtbl1), vtbl = ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
# buf4 = # buf, # buf0 = ENCODED_NAT_SIZE, # buf2 = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), ENCODED_NAT_SIZE + # buf2 + # buf3 = # buf, buf1 = buf0 + buf2 + buf3, subarray(buf4, ENCODED_NAT_SIZE, # buf - ENCODED_NAT_SIZE) = subarray(buf, ENCODED_NAT_SIZE, # buf - ENCODED_NAT_SIZE), vtbl1 ≠ ∅, is-encoded(#(vtbl1 ∪ vtbl), buf0), is-encoded-rec(vtbl, buf2), v ∈ vtbl1, # vtbl1 * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf3, #(vtbl1 ∪ vtbl) * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) + ENCODED_NAT_SIZE ≤ # buf, ENCODED_NAT_SIZE ≤ # buf, vtbl1 ⊥ vtbl, ¬ v ∈ vtbl, err0 = ESUCCESS → is-encoded(#(vtbl1 ∪ vtbl), subarray(buf4, 0, ENCODED_NAT_SIZE)) ∧ n1 = ENCODED_NAT_SIZE, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ ⟪encode_volid#(v, ENCODED_NAT_SIZE + # buf2; buf1, n; err); vtbl0 := vtbl1; n0 := ENCODED_NAT_SIZE + # buf2; if err = ESUCCESS then {n0 := n0 + n; encode_nat#(vtbl0[v], n0; buf1, n; err); n0 := n0 + n}; vtbl0 := vtbl0 -- v⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # buf1 = # buf ∧ ( err = ESUCCESS → (∃ buf0, buf2, buf5, vtbl3. buf1 = buf0 + buf2 + buf5 ∧ vtbl1 ∪ vtbl = vtbl0 ∪ vtbl3 ∧ vtbl0 ⊥ vtbl3 ∧ # buf0 + # buf2 = n0 ∧ # vtbl0 * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf5 ∧ is-encoded(#(vtbl0 ∪ vtbl3), buf0) ∧ is-encoded-rec(vtbl3, buf2))) ∧ # vtbl0 < # 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);%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[encoding-nat-buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)%disjoint-in-left: ⊦ v ∈ vtbl ∧ vtbl ⊥ vtbl0 → ¬ v ∈ vtbl0; (forward) from specification store-union[vtbl]%is-encoded-size: ⊦ is-encoded(n, buf) → # buf = ENCODED_NAT_SIZE; (forward) from specification encoding-fixed-size[encoding-nat]% ⊦ n ≥ m ↔ m ≤ n; (s)