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Proof step 11 from proof encode-node (previous step)

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

User applied rule insert program lemma

And obtained the following new goals

Proof step 12:
n + NODE_HEADER_SIZE ≤ # buf, buf0 = buf ⊦ ⟪encode_header#(ndhd, n; buf; err)⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # buf = # buf0 ∧ subarray(buf, 0, n) = subarray(buf0, 0, n) ∧ subarray(buf, n + NODE_HEADER_SIZE, # buf - n + NODE_HEADER_SIZE) = subarray(buf0, n + NODE_HEADER_SIZE, # buf - n + NODE_HEADER_SIZE) ∧ (err = ESUCCESS → is-encoded(ndhd, subarray(buf, n, NODE_HEADER_SIZE))))
Proof step 13:
# buf = n0 + n + 2 * NODE_HEADER_SIZE + nd.alignedsize, buf = buf, buf1 = buf, buf2 = buf, n1 = n, ndhd0 = nodeheader(node-size-headerless(nd), false), n + 2 * NODE_HEADER_SIZE + nd.alignedsize ≤ # buf, n + NODE_HEADER_SIZE ≤ # buf ⊦ [encode_header#(nodeheader(node-size-headerless(nd), false), n; buf; err)] ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # buf = # buf2 ∧ subarray(buf, 0, n1) = subarray(buf2, 0, n1) ∧ subarray(buf, n1 + NODE_HEADER_SIZE, # buf - n1 + NODE_HEADER_SIZE) = subarray(buf2, n1 + NODE_HEADER_SIZE, # buf - n1 + NODE_HEADER_SIZE) ∧ (err = ESUCCESS → is-encoded(ndhd0, subarray(buf, n1, NODE_HEADER_SIZE))) → ⟪m3 := n; if err = ESUCCESS then encode_node_headerless#(nd, m3 + NODE_HEADER_SIZE; buf, m; err); m0 := align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE); if err = ESUCCESS then {buf := fill(buf, empty, m3 + NODE_HEADER_SIZE + node-size-headerless(nd), m0 - node-size-headerless(nd)); buf := copy(validtrailer, 0, buf, m3 + NODE_HEADER_SIZE + m0, NODE_HEADER_SIZE)}; m2 := 2 * NODE_HEADER_SIZE + m0⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # buf = # buf1 ∧ subarray(buf, 0, n) = subarray(buf1, 0, n) ∧ subarray(buf, n + 2 * NODE_HEADER_SIZE + nd.alignedsize, n0) = subarray(buf1, n + 2 * NODE_HEADER_SIZE + nd.alignedsize, n0) ∧ ( err = ESUCCESS → (∃ buf0, buf1. subarray(buf, n, 2 * NODE_HEADER_SIZE + nd.alignedsize) = buf0 + buf1 + validtrailer ∧ is-encoded(nodeheader(node-size-headerless(nd), false), buf0) ∧ is-encoded(nd, subarray(buf1, 0, node-size-headerless(nd))) ∧ # buf1 = nd.alignedsize) ∧ m2 = 2 * NODE_HEADER_SIZE + nd.alignedsize)))

Rule argument

spec: encoding-fixed-size-nonempty, inst: encoding-node-header name: encode-contract seq: n + NODE_HEADER_SIZE ≤ # buf, buf0 = buf ⊦ ⟪encode_header#(ndhd, n; buf; err)⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # buf = # buf0 ∧ subarray(buf, 0, n) = subarray(buf0, 0, n) ∧ subarray (buf, n + NODE_HEADER_SIZE, # buf - n + NODE_HEADER_SIZE) = subarray (buf0, n + NODE_HEADER_SIZE, # buf - n + NODE_HEADER_SIZE) ∧ ( err = ESUCCESS → is-encoded(ndhd, subarray(buf, n, NODE_HEADER_SIZE)))) subst: [n, ndhd, buf, err, buf0] → [n, nodeheader(node-size-headerless(nd), false), buf, err, buf] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ NODE_HEADER_SIZE + n ≠ 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m * n + n0 < n ↔ m = 0 ∧ n0 < n; (ws)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult