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Proof step 13 from proof prepost-encode-padding (previous step)

# buf = n0 + 2 * NODE_HEADER_SIZE, # buf1 = # buf, subarray(buf1, NODE_HEADER_SIZE, # buf - NODE_HEADER_SIZE) = subarray(buf, NODE_HEADER_SIZE, # buf - NODE_HEADER_SIZE), is-aligned(# buf, 2 * NODE_HEADER_SIZE), 0 + NODE_HEADER_SIZE ≤ # validtrailer, (# buf1 - NODE_HEADER_SIZE) + NODE_HEADER_SIZE ≤ # buf1, NODE_HEADER_SIZE ≤ # buf, # buf1 ≥ NODE_HEADER_SIZE, err = ESUCCESS → is-encoded(nodeheader(n0, true), subarray(buf1, 0, NODE_HEADER_SIZE)), err = ESUCCESS ∨ ⌊err⌋ ⊦ buf = mkbuf(0), (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # copy(validtrailer, 0, buf1, # buf1 - NODE_HEADER_SIZE, NODE_HEADER_SIZE) = # buf ∧ (err = ESUCCESS → abs-padding(copy(validtrailer, 0, buf1, # buf1 - NODE_HEADER_SIZE, NODE_HEADER_SIZE)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
# buf = n0 + 2 * NODE_HEADER_SIZE, # buf1 = # buf, subarray(buf1, NODE_HEADER_SIZE, # buf - NODE_HEADER_SIZE) = subarray(buf, NODE_HEADER_SIZE, # buf - NODE_HEADER_SIZE), is-aligned(# buf, 2 * NODE_HEADER_SIZE), is-encoded(nodeheader(n0, true), subarray(buf1, 0, NODE_HEADER_SIZE)), NODE_HEADER_SIZE ≤ # buf ⊦ buf = mkbuf(0), abs-padding(copy(validtrailer, 0, buf1, # buf - NODE_HEADER_SIZE, NODE_HEADER_SIZE))

Rule argument

Additional information

Used simplifier rules: ⊦ # subarray(buf, m, n) = n; (s)%lfw-is-encoded-nodeheader-size: ⊦ is-encoded(ndhd, buf) → # buf = NODE_HEADER_SIZE; (forward) from specification abs-node[encoding-index-node]% ⊦ # copy(buf, m, buf0, m0, n) = # buf0; (s)% ⊦ # validtrailer = NODE_HEADER_SIZE; (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)%n ≤ m ⊦ (m - n) + m0 ≤ n0 ↔ m + m0 ≤ n0 + n; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ n ≥ m ↔ m ≤ n; (s)