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Proof step 142 from proof abs-nodes-add-crash-aligned-h (previous step)

# buf6 = NODE_HEADER_SIZE, # buf3 = NODE_HEADER_SIZE, # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, # buf0 = a0.alignedsize, buf3 + subarray(buf0 + validtrailer, 0, n0) = buf6 + (buf5 + validtrailer) + buf2, n0 < NODE_HEADER_SIZE + a0.alignedsize + # buf + # buf1, n0 < NODE_HEADER_SIZE + a0.alignedsize, abs-node(buf1, a), abs-nodes (buf2, 2 * NODE_HEADER_SIZE + m + # buf5, 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(n0, NODE_HEADER_SIZE), is-aligned(# buf5, 2 * NODE_HEADER_SIZE), is-encoded(a0, subarray(buf0, 0, node-size-headerless(a0))), is-encoded(nodeheader(node-size-headerless(a0), false), buf3), is-encoded(nodeheader(# buf5, true), buf6), ∀ 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 ⊦ NODE_HEADER_SIZE + a0.alignedsize + # buf + # buf1 = n0, buf3 + buf0 + validtrailer = mkbuf(0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: array-splice, inst: buffer name: append-inj seq: ⊦ # buf = # buf0 → (buf + buf1 = buf0 + buf2 ↔ buf = buf0 ∧ buf1 = buf2) subst: [buf2, buf0, buf1, buf] → [(buf5 + validtrailer) + buf2, buf6, subarray(buf0 + validtrailer, 0, n0), buf3] flags: <all paths>

Additional information

Used simplifier rules: ⊦ is-encoded(ndhd, buf) → (is-encoded(ndhd0, buf) ↔ ndhd = ndhd0); (s)%⊦ nodeheader(m, boolvar) = nodeheader(m0, boolvar0) ↔ m = m0 ∧ (boolvar ↔ boolvar0); (ws)%n = # buf ⊦ subarray(buf + buf0, 0, n) = buf; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ # validtrailer = NODE_HEADER_SIZE; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s) Used terms: (buf5 + validtrailer) + buf2, buf6, subarray(buf0 + validtrailer, 0, n0), buf3