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Proof step 26 from proof abs-nodes-valid-node (previous step)

abs-nodes(buf0, n + # buf1, nd ' + x0, @(m0, m1) ' + lax0, weak), abs-padding(buf1), is-encoded(nodeheader(m, boolvar0), subarray(buf1 + buf0, 0, NODE_HEADER_SIZE)), range=(buf1 + buf0, NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE), validtrailer, 0, NODE_HEADER_SIZE), 2 * NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE) ≤ # buf1 + # buf0 ⊦ ∃ buf3, buf2. buf1 + buf0 = buf3 + buf2 ∧ ( boolvar0 ∧ abs-padding(buf3) ∧ abs-nodes(buf2, n + # buf3, nd ' + x0, @(m0, m1) ' + lax0, weak) ∨ # buf3 = 2 * NODE_HEADER_SIZE + nd.alignedsize ∧ @(m0, m1) = @(n, # buf3) ∧ ¬ boolvar0 ∧ abs-node(buf3, nd) ∧ abs-nodes(buf2, n + # buf3, x0, lax0, weak))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 27:
abs-nodes(buf0, n + # buf1, nd ' + x0, @(m0, m1) ' + lax0, weak), abs-padding(buf1), is-encoded(nodeheader(m, boolvar0), subarray(buf1, 0, NODE_HEADER_SIZE)), range=(buf1 + buf0, NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE), validtrailer, 0, NODE_HEADER_SIZE), 2 * NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE) ≤ # buf1 + # buf0 ⊦ ∃ buf, buf2. buf1 + buf0 = buf + buf2 ∧ ( boolvar0 ∧ buf1 = buf ∧ abs-nodes(buf2, n + 2 * NODE_HEADER_SIZE + m, nd ' + x0, @(m0, m1) ' + lax0, weak) ∨ # buf = 2 * NODE_HEADER_SIZE + nd.alignedsize ∧ @(m0, m1) = @(n, # buf) ∧ ¬ boolvar0 ∧ abs-node(buf, nd) ∧ abs-nodes(buf2, n + # buf, x0, lax0, weak))

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%⊦ abs-padding(buf) ∧ is-encoded (nodeheader(m, true), subarray(buf, 0, NODE_HEADER_SIZE)) → # buf = 2 * NODE_HEADER_SIZE + m; (s)%⊦ buf0 + buf1 = buf2 + buf3 ∧ abs-padding(buf0) → (abs-padding(buf2) ↔ buf0 = buf2); (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]%n + m ≤ # buf ⊦ subarray(buf + buf0, n, m) = subarray(buf, n, m); (s)% ⊦ # buf < NODE_HEADER_SIZE → ¬ abs-padding(buf); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)