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Proof step 83 from proof encode (previous step)

# buf4 = 2 * ENCODED_NAT_SIZE + n0 + # buf2 + ENCODED_VOLID_SIZE, # buf11 = 0, # 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, ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE + n0 = # buf9, ENCODED_NAT_SIZE + # buf2 + # buf9 = # buf4, ENCODED_NAT_SIZE = # buf5, is-encoded(#(vtbl1 ∪ vtbl), buf0), is-encoded(v, subarray(buf0 + buf2 + buf9, 0 + ENCODED_NAT_SIZE + # buf2, ENCODED_VOLID_SIZE)), is-encoded(vtbl1[v], subarray(buf9, ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE)), is-encoded-rec(vtbl, buf2), v ∈ vtbl1, #(vtbl1 ∪ vtbl) * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf2 + # buf9, (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) * m ≤ n0, 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ≤ # buf4, ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ≤ # buf4, 0 + (ENCODED_NAT_SIZE + # buf2) + ENCODED_VOLID_SIZE ≤ #(buf0 + buf2 + buf9), (ENCODED_NAT_SIZE + # buf2) + ENCODED_VOLID_SIZE ≤ (ENCODED_NAT_SIZE + # buf2) + ENCODED_VOLID_SIZE, vtbl1 ⊥ vtbl, err0 = ESUCCESS → is-encoded(#(vtbl1 ∪ vtbl), subarray(buf4, 0, ENCODED_NAT_SIZE)) ∧ n1 = ENCODED_NAT_SIZE, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ vtbl1 = ∅, v ∈ vtbl, ∃ buf6, buf12, buf13, vtbl0. buf0 + buf2 + buf9 = buf6 + buf12 + buf13 ∧ vtbl1 ∪ vtbl = (vtbl1 -- v) ∪ vtbl0 ∧ vtbl1 -- v ⊥ vtbl0 ∧ # buf6 + # buf12 = 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ∧ m * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf13 ∧ is-encoded(#((vtbl1 -- v) ∪ vtbl0), buf6) ∧ is-encoded-rec(vtbl0, buf12)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 84:
# buf10 = 0, # buf3 = 0, # buf2 = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf0 = ENCODED_NAT_SIZE, # buf8 = ENCODED_VOLID_SIZE, # buf = 0, # buf1 = 0, # vtbl1 = m + 1, # buf7 = ENCODED_NAT_SIZE, # buf11 = 0, # buf4 = 2 * ENCODED_NAT_SIZE + n0 + # buf2 + ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE + # buf2 + # buf9 = # buf4, ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE + n0 = # buf9, ENCODED_NAT_SIZE = # buf5, is-encoded(vtbl1[v], subarray(buf9, ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE)), is-encoded(v, subarray(buf9, 0, ENCODED_VOLID_SIZE)), is-encoded(#(vtbl1 ∪ vtbl), buf0), is-encoded-rec(vtbl, buf2), v ∈ vtbl1, ENCODED_VOLID_SIZE ≤ # buf9, ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ≤ # buf4, 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ≤ # buf4, (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) * m ≤ n0, #(vtbl1 ∪ vtbl) * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf2 + # buf9, vtbl1 ⊥ vtbl, err0 = ESUCCESS → is-encoded(#(vtbl1 ∪ vtbl), subarray(buf4, 0, ENCODED_NAT_SIZE)) ∧ n1 = ENCODED_NAT_SIZE, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ vtbl1 = ∅, v ∈ vtbl, ∃ buf6, buf12, buf13, vtbl0. buf0 + buf2 + buf9 = buf6 + buf12 + buf13 ∧ vtbl1 ∪ vtbl = (vtbl1 -- v) ∪ vtbl0 ∧ vtbl1 -- v ⊥ vtbl0 ∧ # buf6 + # buf12 = 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ∧ m * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf13 ∧ is-encoded(#((vtbl1 -- v) ∪ vtbl0), buf6) ∧ is-encoded-rec(vtbl0, buf12)

Rule argument

Additional information

Used simplifier rules: ⊦ # subarray(buf, m, n) = n; (s)% ⊦ m - m = 0; (s)%is-encoded-size: ⊦ is-encoded(v, buf) → # buf = ENCODED_VOLID_SIZE; (forward) from specification encoding-fixed-size[encoding-volid]% ⊦ m + n - m = n; (s)%# buf ≤ n0, n0 + m ≤ # buf + # buf0 ⊦ subarray(buf + buf0, n0, m) = subarray(buf0, n0 - # buf, m); (s)% ⊦ ¬ m + n < m; (s)% ⊦ ENCODED_VOLID_SIZE ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m ≤ m + n; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[encoding-nat-buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ n + 0 = n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m ≤ m; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)