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Proof step 62 from proof encode (previous step)

# vtbl1 = m + 1, # buf3 = ENCODED_VOLID_SIZE + n2, # buf = # buf4, # buf4 = (# buf2 + ENCODED_VOLID_SIZE + n2) + ENCODED_NAT_SIZE, # buf0 = ENCODED_NAT_SIZE, # buf2 = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf5 = # buf4, # buf6 = # buf4, # buf4 = n0 + 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE, subarray(buf4, ENCODED_NAT_SIZE, # buf2 + ENCODED_VOLID_SIZE + n2) = subarray(buf, ENCODED_NAT_SIZE, # buf2 + ENCODED_VOLID_SIZE + n2), 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, subarray(buf6, 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE, n0) = subarray(buf5, 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE, n0), subarray(buf6, 0, (ENCODED_NAT_SIZE + # buf2) + ENCODED_VOLID_SIZE) = subarray(buf5, 0, (ENCODED_NAT_SIZE + # buf2) + ENCODED_VOLID_SIZE), is-encoded(vtbl1[v], subarray(buf6, (ENCODED_NAT_SIZE + # buf2) + ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE)), 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_NAT_SIZE + ENCODED_VOLID_SIZE) * m + ENCODED_NAT_SIZE ≤ n2, ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ≤ # buf4, 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ≤ # buf4, #(vtbl1 ∪ vtbl) * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf2 + ENCODED_VOLID_SIZE + n2, vtbl1 ⊥ vtbl, err0 = ESUCCESS → is-encoded(#(vtbl1 ∪ vtbl), subarray(buf4, 0, ENCODED_NAT_SIZE)) ∧ n1 = ENCODED_NAT_SIZE, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ vtbl1 = ∅, v ∈ vtbl, ∃ buf1, buf7, buf8, vtbl0. buf6 = buf1 + buf7 + buf8 ∧ vtbl1 ∪ vtbl = (vtbl1 -- v) ∪ vtbl0 ∧ vtbl1 -- v ⊥ vtbl0 ∧ # buf1 + # buf7 = 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ∧ m * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf8 ∧ is-encoded(#((vtbl1 -- v) ∪ vtbl0), buf1) ∧ is-encoded-rec(vtbl0, buf7)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 63:
# buf4 = n0 + 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE, # buf6 = # buf4, # buf5 = # buf4, # buf2 = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf0 = ENCODED_NAT_SIZE, # buf = # buf4, # buf3 = ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE + n0, # vtbl1 = m + 1, subarray(buf6, 0, (ENCODED_NAT_SIZE + # buf2) + ENCODED_VOLID_SIZE) = subarray(buf5, 0, (ENCODED_NAT_SIZE + # buf2) + ENCODED_VOLID_SIZE), subarray(buf6, 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE, n0) = subarray(buf5, 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE, n0), subarray(buf5, 0, ENCODED_NAT_SIZE + # buf2) = buf0 + buf2, subarray(buf5, ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE + n0) = subarray(buf3, ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE + n0), subarray(buf4, ENCODED_NAT_SIZE, # buf2 + # buf3) = subarray(buf, ENCODED_NAT_SIZE, # buf2 + # buf3), is-encoded(v, subarray(buf5, ENCODED_NAT_SIZE + # buf2, ENCODED_VOLID_SIZE)), is-encoded(#(vtbl1 ∪ vtbl), buf0), is-encoded(vtbl1[v], subarray(buf6, (ENCODED_NAT_SIZE + # buf2) + ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE)), is-encoded-rec(vtbl, buf2), v ∈ vtbl1, #(vtbl1 ∪ vtbl) * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf2 + # buf3, 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ≤ # buf4, ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ≤ # buf4, (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) * m ≤ n0, vtbl1 ⊥ vtbl, err0 = ESUCCESS → is-encoded(#(vtbl1 ∪ vtbl), subarray(buf4, 0, ENCODED_NAT_SIZE)) ∧ n1 = ENCODED_NAT_SIZE, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ vtbl1 = ∅, v ∈ vtbl, ∃ buf1, buf7, buf8, vtbl0. buf6 = buf1 + buf7 + buf8 ∧ vtbl1 ∪ vtbl = (vtbl1 -- v) ∪ vtbl0 ∧ vtbl1 -- v ⊥ vtbl0 ∧ # buf1 + # buf7 = 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ∧ m * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf8 ∧ is-encoded(#((vtbl1 -- v) ∪ vtbl0), buf1) ∧ is-encoded-rec(vtbl0, buf7)

Rule argument

Additional information

Used simplifier rules: ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m + m = 2 * m; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ m0 * 1 = m0; (s)%m2 ≠ 0 ⊦ (* m2) * m + n = m + n0 ↔ (m2 - 1) * m + 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