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Proof step 18 from proof encode-node (previous step)

# buf0 = # buf, # buf = n0 + n + 2 * NODE_HEADER_SIZE + nd.alignedsize, err = ESUCCESS, m3 = n, subarray(buf0, 0, n) = subarray(buf, 0, n), subarray(buf0, n + NODE_HEADER_SIZE, # buf - n + NODE_HEADER_SIZE) = subarray(buf, n + NODE_HEADER_SIZE, # buf - n + NODE_HEADER_SIZE), n + NODE_HEADER_SIZE ≤ # buf, n + 2 * NODE_HEADER_SIZE + nd.alignedsize ≤ # buf, err = ESUCCESS → is-encoded(nodeheader(node-size-headerless(nd), false), subarray(buf0, n, NODE_HEADER_SIZE)), err = ESUCCESS ∨ ⌊err⌋ ⊦ ⟪encode_node_headerless#(nd, m3 + NODE_HEADER_SIZE; buf0, m; err); m0 := align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE); if err = ESUCCESS then {buf0 := fill(buf0, empty, m3 + NODE_HEADER_SIZE + node-size-headerless(nd), m0 - node-size-headerless(nd)); buf0 := copy(validtrailer, 0, buf0, m3 + NODE_HEADER_SIZE + m0, NODE_HEADER_SIZE)}; m2 := 2 * NODE_HEADER_SIZE + m0⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # buf0 = # buf ∧ subarray(buf0, 0, n) = subarray(buf, 0, n) ∧ subarray(buf0, n + 2 * NODE_HEADER_SIZE + nd.alignedsize, n0) = subarray(buf, n + 2 * NODE_HEADER_SIZE + nd.alignedsize, n0) ∧ ( err = ESUCCESS → (∃ buf2, buf1. subarray(buf0, n, 2 * NODE_HEADER_SIZE + nd.alignedsize) = buf2 + buf1 + validtrailer ∧ is-encoded(nodeheader(node-size-headerless(nd), false), buf2) ∧ is-encoded(nd, subarray(buf1, 0, node-size-headerless(nd))) ∧ # buf1 = nd.alignedsize) ∧ m2 = 2 * NODE_HEADER_SIZE + nd.alignedsize))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
# buf0 = # buf, # buf = n0 + n + 2 * NODE_HEADER_SIZE + nd.alignedsize, subarray(buf0, 0, n) = subarray(buf, 0, n), subarray(buf0, n + NODE_HEADER_SIZE, # buf - n + NODE_HEADER_SIZE) = subarray(buf, n + NODE_HEADER_SIZE, # buf - n + NODE_HEADER_SIZE), is-encoded(nodeheader(node-size-headerless(nd), false), subarray(buf0, n, NODE_HEADER_SIZE)), n + NODE_HEADER_SIZE ≤ # buf, n + 2 * NODE_HEADER_SIZE + nd.alignedsize ≤ # buf ⊦ ⟪encode_node_headerless#(nd, n + NODE_HEADER_SIZE; buf0, m; err); m0 := align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE); if err = ESUCCESS then {buf0 := fill(buf0, empty, n + NODE_HEADER_SIZE + node-size-headerless(nd), m0 - node-size-headerless(nd)); buf0 := copy(validtrailer, 0, buf0, n + NODE_HEADER_SIZE + m0, NODE_HEADER_SIZE)}; m2 := 2 * NODE_HEADER_SIZE + m0⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # buf0 = # buf ∧ subarray(buf0, 0, n) = subarray(buf, 0, n) ∧ subarray(buf0, n + 2 * NODE_HEADER_SIZE + nd.alignedsize, n0) = subarray(buf, n + 2 * NODE_HEADER_SIZE + nd.alignedsize, n0) ∧ ( err = ESUCCESS → (∃ buf2, buf1. subarray(buf0, n, 2 * NODE_HEADER_SIZE + nd.alignedsize) = buf2 + buf1 + validtrailer ∧ is-encoded(nodeheader(node-size-headerless(nd), false), buf2) ∧ is-encoded(nd, subarray(buf1, 0, node-size-headerless(nd))) ∧ # buf1 = nd.alignedsize) ∧ m2 = 2 * NODE_HEADER_SIZE + nd.alignedsize))

Rule argument

Additional information

Used simplifier rules: ⊦ # subarray(buf, m, n) = n; (s)%is-encoded-size: ⊦ is-encoded(ndhd, buf) → # buf = NODE_HEADER_SIZE; (forward) from specification encoding-fixed-size-nonempty[encoding-node-header]