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Proof step 128 from proof abs-nodes-add-crash-aligned-h (previous step)

# buf3 = NODE_HEADER_SIZE, # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, # buf0 = a0.alignedsize, n < 2 * NODE_HEADER_SIZE + a0.alignedsize + # buf + # buf1, n < 2 * NODE_HEADER_SIZE + a0.alignedsize, abs-node(buf1, a), abs-nodes (subarray(buf3 + buf0 + validtrailer, 0, n), m, (a0 ' + x0) + a ', @(m, 2 * NODE_HEADER_SIZE + a0.alignedsize) ' + lax0 + @(2 * NODE_HEADER_SIZE + m + a0.alignedsize + # buf, # buf1) ', boolvar), abs-nodes(buf, 2 * NODE_HEADER_SIZE + m + a0.alignedsize, x0, lax0, false), is-aligned(m, NODE_HEADER_SIZE), is-aligned(n, NODE_HEADER_SIZE), is-encoded(a0, subarray(buf0, 0, node-size-headerless(a0))), is-encoded(nodeheader(node-size-headerless(a0), false), buf3), ∀ buf4, buf1, a, n, m, x, lax, boolvar. # buf4 < #((buf3 + buf0 + validtrailer) + buf) → # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n < # buf4 + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes(subarray(buf4 + buf1, 0, n), m, x + a ', lax + @(m + # buf4, # buf1) ', boolvar) ∧ abs-nodes(buf4, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → n = # buf4 + # buf1 ⊦ buf3 + buf0 + validtrailer = mkbuf(0), n = 2 * NODE_HEADER_SIZE + a0.alignedsize + # buf + # buf1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 129:
⊦ abs-nodes(buf, m, a ' + x, lax, weak) ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf1, m + # buf0, a ' + x, lax, weak) ∨ lax ≠ [] ∧ lax.head.off = m ∧ lax.head.size = # buf0 ∧ abs-node(buf0, a) ∧ abs-nodes(buf1, m + # buf0, x, lax.tail, weak)))
Proof step 130:
# buf0 = a0.alignedsize, # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, # buf3 = NODE_HEADER_SIZE, n < 2 * NODE_HEADER_SIZE + a0.alignedsize, n < 2 * NODE_HEADER_SIZE + a0.alignedsize + # buf + # buf1, abs-node(buf1, a), abs-nodes(buf, 2 * NODE_HEADER_SIZE + m + a0.alignedsize, x0, lax0, false), is-aligned(n, NODE_HEADER_SIZE), is-aligned(m, NODE_HEADER_SIZE), is-encoded(nodeheader(node-size-headerless(a0), false), buf3), is-encoded(a0, subarray(buf0, 0, node-size-headerless(a0))), ∃ buf2, buf4. subarray(buf3 + buf0 + validtrailer, 0, n) = buf2 + buf4 ∧ ( abs-padding(buf2) ∧ abs-nodes (buf4, m + # buf2, a0 ' + x0 + a ', @(m, 2 * NODE_HEADER_SIZE + a0.alignedsize) ' + lax0 + @(2 * NODE_HEADER_SIZE + m + a0.alignedsize + # buf, # buf1) ', boolvar) ∨ @(m, 2 * NODE_HEADER_SIZE + a0.alignedsize) ' + lax0 + @(2 * NODE_HEADER_SIZE + m + a0.alignedsize + # buf, # buf1) ' ≠ [] ∧ (@(m, 2 * NODE_HEADER_SIZE + a0.alignedsize) ' + lax0 + @(2 * NODE_HEADER_SIZE + m + a0.alignedsize + # buf, # buf1) ').head.off = m ∧ (@(m, 2 * NODE_HEADER_SIZE + a0.alignedsize) ' + lax0 + @(2 * NODE_HEADER_SIZE + m + a0.alignedsize + # buf, # buf1) ').head.size = # buf2 ∧ abs-node(buf2, a0) ∧ abs-nodes (buf4, m + # buf2, x0 + a ', (@(m, 2 * NODE_HEADER_SIZE + a0.alignedsize) ' + lax0 + @(2 * NODE_HEADER_SIZE + m + a0.alignedsize + # buf, # buf1) ').tail, boolvar)), ∀ buf4, buf1, a, n, m, x, lax, boolvar. # buf4 < #((buf3 + buf0 + validtrailer) + buf) → # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n < # buf4 + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes(subarray(buf4 + buf1, 0, n), m, x + a ', lax + @(m + # buf4, # buf1) ', boolvar) ∧ abs-nodes(buf4, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → n = # buf4 + # buf1 ⊦ buf3 + buf0 + validtrailer = mkbuf(0), n = 2 * NODE_HEADER_SIZE + a0.alignedsize + # buf + # buf1

Rule argument

spec: <toplevel> name: abs-nodes-rec seq: ⊦ abs-nodes(buf, m, a ' + x, lax, weak) ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf1, m + # buf0, a ' + x, lax, weak) ∨ lax ≠ [] ∧ lax.head.off = m ∧ lax.head.size = # buf0 ∧ abs-node(buf0, a) ∧ abs-nodes(buf1, m + # buf0, x, lax.tail, weak))) subst: [weak, lax, x, a, m, buf] → [boolvar, @(m, 2 * NODE_HEADER_SIZE + a0.alignedsize) ' + lax0 + @ (2 * NODE_HEADER_SIZE + m + a0.alignedsize + # buf, # buf1) ', x0 + a ', a0, m, subarray(buf3 + buf0 + validtrailer, 0, n)] flags: <all paths>

Additional information

Used simplifier rules: append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]%a: ⊦ (x + y) + z = x + y + z; from specification list%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list] Used terms: boolvar, @(m, 2 * NODE_HEADER_SIZE + a0.alignedsize) ' + lax0 + @(2 * NODE_HEADER_SIZE + m + a0.alignedsize + # buf, # buf1) ', x0 + a ', a0, m, subarray(buf3 + buf0 + validtrailer, 0, n)