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Proof step 27 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, 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))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: abs-node name: abs-padding seq: ⊦ abs-padding(buf) ↔ (∃ buf0, buf1. buf = buf0 + buf1 + validtrailer ∧ is-encoded(nodeheader(# buf1, true), buf0) ∧ is-aligned(# buf1, 2 * NODE_HEADER_SIZE)) subst: [buf] → [buf1] flags: <all paths>

Additional information

Used simplifier rules: abs-nodes-mkbuf0-empty-h: ⊦ abs-nodes(mkbuf(0), m, x, lax, weak) ↔ x = [] ∧ lax = [];%abs-nodes-headerspace: # buf ≠ 0 ⊦ abs-nodes(buf, m, x, lax, weak) → (NODE_HEADER_SIZE ≤ # buf + n ↔ NODE_HEADER_SIZE ≤ # buf);% ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ # validtrailer = NODE_HEADER_SIZE; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%m2 ≠ 0 ⊦ (* m2) * m + n ≤ m + n0 ↔ (m2 - 1) * m + n ≤ n0; (s)% ⊦ m0 * 1 = m0; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%c: ⊦ m + n = n + m; from specification nat-basic%lfw-is-encoded-nodeheader-size: ⊦ is-encoded(ndhd, buf) → # buf = NODE_HEADER_SIZE; (forward) from specification abs-node%n = # buf ⊦ subarray(buf + buf0, 0, n) = buf; (s)% ⊦ is-encoded(ndhd, buf) → (is-encoded(ndhd0, buf) ↔ ndhd = ndhd0); (s)%⊦ nodeheader(m, boolvar) = nodeheader(m0, boolvar0) ↔ m = m0 ∧ (boolvar ↔ boolvar0); (ws)% ⊦ 2 * m = 0 ↔ m = 0; (s)% ⊦ NODE_HEADER_SIZE ≠ 0; (s)%m ≠ 0 ⊦ is-aligned(n, m) → n % m = 0; (s)%n ≠ 0, m % n = 0 ⊦ align↑(m, n) = m; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ # buf = 0 ↔ buf = mkbuf(0); (s)% ⊦ a ' + x ≠ []; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ buf + buf0 = buf + buf1 ↔ buf0 = buf1; (s)% ⊦ m + m = 2 * m; (s) Used terms: buf1