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Proof step 33 from proof abs-nodes-valid-node (previous step)

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, boolvar0 ∧ abs-padding(buf1) ∧ abs-nodes(buf0, n + # buf1, nd ' + x0, @(m0, m1) ' + lax0, weak) ∨ # buf1 = 2 * NODE_HEADER_SIZE + nd.alignedsize ∧ @(m0, m1) = @(n, # buf1) ∧ ¬ boolvar0 ∧ abs-node(buf1, nd) ∧ abs-nodes(buf0, n + # buf1, x0, lax0, weak) ⊦ ∃ buf3, buf2. buf1 + buf0 = buf3 + buf2 ∧ ( abs-padding(buf3) ∧ abs-nodes(buf2, n + # buf3, nd ' + x0, @(m0, m1) ' + lax0, weak) ∨ m0 = n ∧ m1 = # buf3 ∧ abs-node(buf3, nd) ∧ abs-nodes(buf2, n + # buf3, x0, lax0, weak))

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: left 4

Additional information

Used simplifier rules: ls-abs-node-buf-size: ⊦ abs-node(buf, nd) → # buf = nd.alignedsize + 2 * NODE_HEADER_SIZE;% ⊦ @(m, m0) = @(m1, m2) ↔ m = m1 ∧ m0 = m2; (ws)% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ 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% ⊦ NODE_HEADER_SIZE ≠ 0; (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%n + m ≤ # buf ⊦ subarray(buf + buf0, n, m) = subarray(buf, n, m); (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ abs-node(buf0, nd) ∧ buf0 + buf1 = buf + buf2 → ¬ abs-padding(buf); (s)%⊦ abs-node(buf0, nd0) ∧ buf0 + buf2 = buf1 + buf3 → (abs-node(buf1, nd1) ↔ buf0 = buf1 ∧ nd0 = nd1); (s)% ⊦ buf + buf0 = buf + buf1 ↔ buf0 = buf1; (s)