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Proof step 44 from proof encode (previous step)

# buf = # buf4, # buf4 = (# buf2 + # buf3) + ENCODED_NAT_SIZE, # buf0 = ENCODED_NAT_SIZE, # buf2 = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf5 = # buf4, # buf4 = n2 + ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE, n = ENCODED_VOLID_SIZE, subarray(buf4, ENCODED_NAT_SIZE, # buf2 + # buf3) = subarray(buf, ENCODED_NAT_SIZE, # buf2 + # buf3), subarray(buf5, ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE, n2) = subarray(buf3, ENCODED_VOLID_SIZE, n2), subarray(buf5, 0, ENCODED_NAT_SIZE + # buf2) = buf0 + buf2, is-encoded(#(vtbl1 ∪ vtbl), buf0), is-encoded(v, subarray(buf5, ENCODED_NAT_SIZE + # buf2, ENCODED_VOLID_SIZE)), is-encoded-rec(vtbl, buf2), v ∈ vtbl1, ENCODED_VOLID_SIZE ≤ # buf3, #(vtbl1 ∪ vtbl) * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf2 + # buf3, # vtbl1 * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf3, ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ≤ # buf4, vtbl1 ⊥ vtbl, err0 = ESUCCESS → is-encoded(#(vtbl1 ∪ vtbl), subarray(buf4, 0, ENCODED_NAT_SIZE)) ∧ n1 = ENCODED_NAT_SIZE, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ ⟪encode_nat#(vtbl1[v], (ENCODED_NAT_SIZE + # buf2) + ENCODED_VOLID_SIZE; buf5, n; err); n0 := ((ENCODED_NAT_SIZE + # buf2) + ENCODED_VOLID_SIZE) + n; vtbl0 := vtbl1 -- v⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # buf5 = # buf4 ∧ ( err = ESUCCESS → (∃ buf0, buf2, buf, vtbl3. buf5 = buf0 + buf2 + buf ∧ vtbl1 ∪ vtbl = vtbl0 ∪ vtbl3 ∧ vtbl0 ⊥ vtbl3 ∧ # buf0 + # buf2 = n0 ∧ # vtbl0 * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf ∧ is-encoded(#(vtbl0 ∪ vtbl3), buf0) ∧ is-encoded-rec(vtbl3, buf2))) ∧ # vtbl0 < # vtbl1), vtbl1 = ∅, v ∈ vtbl

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 45:
# buf5 = # buf4, # buf2 = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf0 = ENCODED_NAT_SIZE, # buf4 = (# buf2 + ENCODED_VOLID_SIZE + n2) + ENCODED_NAT_SIZE, # buf = # buf4, # buf3 = ENCODED_VOLID_SIZE + n2, n = ENCODED_VOLID_SIZE, subarray(buf5, 0, ENCODED_NAT_SIZE + # buf2) = buf0 + buf2, subarray(buf5, ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE, n2) = subarray(buf3, ENCODED_VOLID_SIZE, n2), subarray(buf4, ENCODED_NAT_SIZE, # buf2 + ENCODED_VOLID_SIZE + n2) = subarray(buf, ENCODED_NAT_SIZE, # buf2 + ENCODED_VOLID_SIZE + n2), vtbl1 ≠ ∅, is-encoded(v, subarray(buf5, ENCODED_NAT_SIZE + # buf2, ENCODED_VOLID_SIZE)), is-encoded(#(vtbl1 ∪ vtbl), buf0), is-encoded-rec(vtbl, buf2), v ∈ vtbl1, ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ≤ # buf4, # vtbl1 * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ ENCODED_VOLID_SIZE + n2, #(vtbl1 ∪ vtbl) * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf2 + ENCODED_VOLID_SIZE + n2, vtbl1 ⊥ vtbl, ¬ v ∈ vtbl, err0 = ESUCCESS → is-encoded(#(vtbl1 ∪ vtbl), subarray(buf4, 0, ENCODED_NAT_SIZE)) ∧ n1 = ENCODED_NAT_SIZE, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ ⟪encode_nat#(vtbl1[v], (ENCODED_NAT_SIZE + # buf2) + ENCODED_VOLID_SIZE; buf5, n; err); n0 := ((ENCODED_NAT_SIZE + # buf2) + ENCODED_VOLID_SIZE) + n; vtbl0 := vtbl1 -- v⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # buf5 = # buf4 ∧ ( err = ESUCCESS → (∃ buf0, buf2, buf, vtbl3. buf5 = buf0 + buf2 + buf ∧ vtbl1 ∪ vtbl = vtbl0 ∪ vtbl3 ∧ vtbl0 ⊥ vtbl3 ∧ # buf0 + # buf2 = n0 ∧ # vtbl0 * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf ∧ is-encoded(#(vtbl0 ∪ vtbl3), buf0) ∧ is-encoded-rec(vtbl3, buf2))) ∧ # vtbl0 < # vtbl1)

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m + n; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)%eqs: ⊦ m = n + n0 ∧ m = n + n1 → n0 = n1; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic