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Proof step 82 from proof abs-nodes-add-crash-aligned-h (previous step)

# buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, lax.head = @(m0, m1), n < (# buf2 + # buf) + # buf1, abs-node(buf1, a), abs-nodes(subarray(buf2 + buf + buf1, 0, n), m, (a0 ' + x0) + a ', lax + @(m + # buf2 + # buf, # buf1) ', boolvar), is-aligned(m, NODE_HEADER_SIZE), is-aligned(n, NODE_HEADER_SIZE), abs-padding(buf2) ∧ abs-nodes(buf, m + # buf2, a0 ' + x0, lax, false) ∨ lax ≠ [] ∧ m0 = m ∧ m1 = # buf2 ∧ abs-node(buf2, a0) ∧ abs-nodes(buf, m + # buf2, x0, lax.tail, false), ∀ buf3, buf1, a, n, m, x, lax, boolvar. # buf3 < #(buf2 + buf) → # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n < # buf3 + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes(subarray(buf3 + buf1, 0, n), m, x + a ', lax + @(m + # buf3, # buf1) ', boolvar) ∧ abs-nodes(buf3, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → n = # buf3 + # buf1 ⊦ n = (# buf2 + # buf) + # buf1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 83:
⊦ # buf ≤ m ∧ m ≤ # buf + # buf0 → subarray(buf + buf0, 0, m) = buf + subarray(buf0, 0, m - # buf)
Proof step 84:
# buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, lax.head = @(m0, m1), n < (# buf2 + # buf) + # buf1, abs-node(buf1, a), abs-nodes(subarray(buf2 + buf + buf1, 0, n), m, (a0 ' + x0) + a ', lax + @(m + # buf2 + # buf, # buf1) ', boolvar), is-aligned(n, NODE_HEADER_SIZE), is-aligned(m, NODE_HEADER_SIZE), abs-padding(buf2) ∧ abs-nodes(buf, m + # buf2, a0 ' + x0, lax, false) ∨ lax ≠ [] ∧ m0 = m ∧ m1 = # buf2 ∧ abs-node(buf2, a0) ∧ abs-nodes(buf, m + # buf2, x0, lax.tail, false), ∀ buf3, buf1, a, n, m, x, lax, boolvar. # buf3 < #(buf2 + buf) → # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n < # buf3 + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes(subarray(buf3 + buf1, 0, n), m, x + a ', lax + @(m + # buf3, # buf1) ', boolvar) ∧ abs-nodes(buf3, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → n = # buf3 + # buf1 ⊦ n = (# buf2 + # buf) + # buf1, # buf2 ≤ n ∧ n ≤ # buf2 + #(buf + buf1)
Proof step 157:
# buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, lax.head = @(m0, m1), n < (# buf2 + # buf) + # buf1, abs-node(buf1, a), abs-nodes(buf2 + subarray(buf + buf1, 0, n - # buf2), m, (a0 ' + x0) + a ', lax + @(m + # buf2 + # buf, # buf1) ', boolvar), is-aligned(n, NODE_HEADER_SIZE), is-aligned(m, NODE_HEADER_SIZE), # buf2 ≤ n, n ≤ # buf2 + #(buf + buf1), abs-padding(buf2) ∧ abs-nodes(buf, m + # buf2, a0 ' + x0, lax, false) ∨ lax ≠ [] ∧ m0 = m ∧ m1 = # buf2 ∧ abs-node(buf2, a0) ∧ abs-nodes(buf, m + # buf2, x0, lax.tail, false), ∀ buf3, buf1, a, n, m, x, lax, boolvar. # buf3 < #(buf2 + buf) → # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n < # buf3 + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes(subarray(buf3 + buf1, 0, n), m, x + a ', lax + @(m + # buf3, # buf1) ', boolvar) ∧ abs-nodes(buf3, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → n = # buf3 + # buf1 ⊦ n = (# buf2 + # buf) + # buf1

Rule argument

spec: array-splice, inst: buffer name: subarray-append-shift-right seq: ⊦ # buf ≤ m ∧ m ≤ # buf + # buf0 → subarray(buf + buf0, 0, m) = buf + subarray(buf0, 0, m - # buf) subst: [m, buf0, buf] → [n, buf + buf1, buf2] flags: <all paths>

Additional information

Used terms: n, buf + buf1, buf2