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Proof step 74 from proof encode (previous step)

# buf6 = # buf4, # buf4 = n0 + # buf9, # buf7 = ENCODED_NAT_SIZE, # vtbl1 = m + 1, # buf1 = 0, # buf = 0, # buf9 = 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE, # buf8 = ENCODED_VOLID_SIZE, # buf0 = ENCODED_NAT_SIZE, # buf2 = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf3 = 0, subarray(buf9, 0, ENCODED_NAT_SIZE + # buf2) = buf0 + buf2, is-encoded(v, subarray(buf9, 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-rec(vtbl, buf2), v ∈ vtbl1, #(vtbl1 ∪ vtbl) * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf2 + ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE + n0, (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) * m ≤ n0, ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ≤ # buf4, # buf9 ≤ # buf4, 0 + (ENCODED_NAT_SIZE + # buf2) + ENCODED_VOLID_SIZE ≤ # buf9, vtbl1 ⊥ vtbl, err0 = ESUCCESS → is-encoded(#(vtbl1 ∪ vtbl), subarray(buf4, 0, ENCODED_NAT_SIZE)) ∧ n1 = ENCODED_NAT_SIZE, ∃ buf1, buf3. buf9 = buf1 + subarray(buf6, 0, (ENCODED_NAT_SIZE + # buf2) + ENCODED_VOLID_SIZE) + buf3 ∧ # buf1 = 0 ∧ # subarray(buf6, 0, (ENCODED_NAT_SIZE + # buf2) + ENCODED_VOLID_SIZE) = (ENCODED_NAT_SIZE + # buf2) + ENCODED_VOLID_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 = # buf9 ∧ 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 75:
# buf7 = ENCODED_NAT_SIZE, # vtbl1 = m + 1, # buf1 = 0, # buf = 0, # buf8 = ENCODED_VOLID_SIZE, # buf0 = ENCODED_NAT_SIZE, # buf2 = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf3 = 0, # buf10 = 0, # buf6 = # buf4, # buf4 = 2 * ENCODED_NAT_SIZE + n0 + # buf2 + ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE = # buf5, subarray(subarray(buf6, 0, (ENCODED_NAT_SIZE + # buf2) + ENCODED_VOLID_SIZE), 0, ENCODED_NAT_SIZE + # buf2) = buf0 + buf2, is-encoded(v, subarray(subarray(buf6, 0, (ENCODED_NAT_SIZE + # buf2) + ENCODED_VOLID_SIZE), 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-rec(vtbl, buf2), v ∈ vtbl1, #(vtbl1 ∪ vtbl) * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf2 + ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE + n0, (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) * m ≤ n0, ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ≤ # buf4, 2 * 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⌋ ⊦ vtbl1 = ∅, v ∈ vtbl, ∃ buf9, buf11, buf12, vtbl0. buf6 = buf9 + buf11 + buf12 ∧ vtbl1 ∪ vtbl = (vtbl1 -- v) ∪ vtbl0 ∧ vtbl1 -- v ⊥ vtbl0 ∧ # buf9 + # buf11 = 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ∧ m * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf12 ∧ is-encoded(#((vtbl1 -- v) ∪ vtbl0), buf9) ∧ is-encoded-rec(vtbl0, buf11)

Rule argument

Additional information

Used simplifier rules: ⊦ m + m = 2 * m; (s)%is-encoded-size: ⊦ is-encoded(v, buf) → # buf = ENCODED_VOLID_SIZE; (forward) from specification encoding-fixed-size[encoding-volid]% ⊦ ¬ n < n; (s)% ⊦ m ≤ m + n; (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 = m + n0 ↔ (m2 - 1) * m = n0; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)%n + m ≤ # buf ⊦ subarray(buf + buf0, n, m) = subarray(buf, n, m); (s)% ⊦ ¬ m + n < m; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ n + 0 = n; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[encoding-nat-buffer]% ⊦ # buf = 0 → buf + buf0 = buf0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)% ⊦ # subarray(buf, m, n) = n; (s)