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Proof step 35 from proof encode (previous step)

# buf2 = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf0 = ENCODED_NAT_SIZE, # buf4 = (# buf2 + # buf3) + ENCODED_NAT_SIZE, # buf = # buf4, buf1 = buf0 + buf2 + buf3, buf1 = buf1, buf5 = buf1, n2 = ENCODED_NAT_SIZE + # buf2, subarray(buf4, ENCODED_NAT_SIZE, # buf2 + # buf3) = subarray(buf, ENCODED_NAT_SIZE, # buf2 + # buf3), v0 = v, 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) ≤ # buf2 + # buf3, (ENCODED_NAT_SIZE + # buf2) + encoding-size(v) ≤ # buf1, vtbl1 ⊥ 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)] ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # buf1 = # buf5 ∧ subarray(buf1, 0, n2) = subarray(buf5, 0, n2) ∧ subarray(buf1, n2 + encoding-size(v0), # buf1 - n2 + encoding-size(v0)) = subarray(buf5, n2 + encoding-size(v0), # buf1 - n2 + encoding-size(v0)) ∧ (err = ESUCCESS → is-encoded(v0, subarray(buf1, n2, encoding-size(v0))) ∧ n = encoding-size(v0)) → ⟪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 = # buf4 ∧ ( 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)), vtbl1 = ∅, v ∈ vtbl

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ m + n - m = n; (s)%# buf ≤ n0, n0 + m ≤ # buf + # buf0 ⊦ subarray(buf + buf0, n0, m) = subarray(buf0, n0 - # buf, m); (s)% ⊦ ¬ n < n; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%n ≤ m ⊦ (m - n) + m0 ≤ n0 ↔ m + m0 ≤ n0 + n; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m < n → n ≠ 0; (s)%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)%n = # buf ⊦ subarray(buf + buf0, 0, n) = buf; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[encoding-nat-buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ encoding-size(v) = ENCODED_VOLID_SIZE; (s)