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Proof step 113 from proof decode-node (previous step)

# buf = NODE_HEADER_SIZE, # buf1 = align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), is-encoded(nd, subarray(buf1 + buf2, 0, node-size-headerless(nd))), is-encoded(nodeheader(node-size-headerless(nd), false), buf), node-size-headerless(nd) ≤ # buf1 + # buf2, NODE_HEADER_SIZE ≤ # buf2, 0 + NODE_HEADER_SIZE ≤ # buf2, ∃ buf1, buf3. buf2 = buf1 + validtrailer + buf3 ∧ # buf1 = 0 ∧ # validtrailer = NODE_HEADER_SIZE ⊦ ∃ buf0, buf3. buf + buf1 = buf0 + buf3 ∧ is-encoded(nodeheader(node-size-headerless(nd), false), buf0) ∧ is-encoded(nd, subarray(buf3, 0, node-size-headerless(nd))) ∧ # buf3 = # buf1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 114:
# buf = NODE_HEADER_SIZE, # buf1 = align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), is-encoded(nodeheader(node-size-headerless(nd), false), buf), is-encoded(nd, subarray(buf1 + validtrailer + buf0, 0, node-size-headerless(nd))), node-size-headerless(nd) ≤ # buf1 + NODE_HEADER_SIZE + # buf0 ⊦ ∃ buf0, buf3. buf + buf1 = buf0 + buf3 ∧ is-encoded(nodeheader(node-size-headerless(nd), false), buf0) ∧ is-encoded(nd, subarray(buf3, 0, node-size-headerless(nd))) ∧ # buf3 = # buf1

Rule argument

Additional information

Used simplifier rules: buf-size-zero: ⊦ # buf = 0 ↔ buf = mkbuf(0);% ⊦ mkbuf(0) + buf = buf; (s)% ⊦ # mkbuf(n) = n; (s)% ⊦ m ≤ m + n; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ # validtrailer = NODE_HEADER_SIZE; (s)