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Proof step 41 from proof abs-nodes-add-crash-aligned-h (previous step)

# buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, n < (# buf + # buf2) + # buf1, abs-node(buf1, a), abs-nodes(buf2, m + # buf, [], [], false), abs-nodes(subarray(buf + buf2 + buf1, 0, n), m, a ', @(m + # buf + # buf2, # buf1) ', boolvar), abs-padding(buf), is-aligned(n, NODE_HEADER_SIZE), is-aligned(m, NODE_HEADER_SIZE), ∀ buf3, buf1, a, n, m, x, lax, boolvar. # buf3 < #(buf + buf2) → # 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 = (# buf + # buf2) + # buf1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 42:
⊦ # buf ≤ m ∧ m ≤ # buf + # buf0 → subarray(buf + buf0, 0, m) = buf + subarray(buf0, 0, m - # buf)
Proof step 43:
# buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, n < (# buf + # buf2) + # buf1, abs-node(buf1, a), abs-nodes(subarray(buf + buf2 + buf1, 0, n), m, a ', @(m + # buf + # buf2, # buf1) ', boolvar), abs-nodes(buf2, m + # buf, [], [], false), abs-padding(buf), is-aligned(m, NODE_HEADER_SIZE), is-aligned(n, NODE_HEADER_SIZE), ∀ buf3, buf1, a, n, m, x, lax, boolvar. # buf3 < #(buf + buf2) → # 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 = (# buf + # buf2) + # buf1, # buf ≤ n ∧ n ≤ # buf + #(buf2 + buf1)
Proof step 67:
# buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, n < (# buf + # buf2) + # buf1, abs-node(buf1, a), abs-nodes(buf + subarray(buf2 + buf1, 0, n - # buf), m, a ', @(m + # buf + # buf2, # buf1) ', boolvar), abs-nodes(buf2, m + # buf, [], [], false), abs-padding(buf), is-aligned(m, NODE_HEADER_SIZE), is-aligned(n, NODE_HEADER_SIZE), # buf ≤ n, n ≤ # buf + #(buf2 + buf1), ∀ buf3, buf1, a, n, m, x, lax, boolvar. # buf3 < #(buf + buf2) → # 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 = (# buf + # buf2) + # 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, buf2 + buf1, buf] flags: <all paths>

Additional information

Used terms: n, buf2 + buf1, buf