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Proof step 51 from proof abs-nodes-unique-weak-h (previous step)

# buf1 = nd.alignedsize + 2 * NODE_HEADER_SIZE, abs-node(buf1, nd), abs-nodes(buf0, m + # buf1, x, lax2, true), ∃ buf3, buf2. buf1 + buf0 = buf3 + buf2 ∧ ( abs-padding(buf3) ∧ abs-nodes(buf2, m + # buf3, nd0 ' + x2, lax1, true) ∨ lax1 ≠ [] ∧ lax1.head.off = m ∧ lax1.head.size = # buf3 ∧ abs-node(buf3, nd0) ∧ abs-nodes(buf2, m + # buf3, x2, lax1.tail, true)), ∀ buf2, m, x0, lax0, x1, lax1. # buf2 < #(buf1 + buf0) → abs-nodes(buf2, m, x0, lax0, true) ∧ abs-nodes(buf2, m, x1, lax1, true) → x0 = x1 ∧ lax0 = lax1 ⊦ nd ' + x = nd0 ' + x2 ∧ @(m, # buf1) ' + lax2 = lax1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 52:
# buf2 = nd.alignedsize + 2 * NODE_HEADER_SIZE, lax1.head.size = # buf2, abs-node(buf2, nd), abs-nodes(buf, lax1.head.off + # buf2, x, lax2, true), abs-nodes(buf, lax1.head.off + # buf2, x2, lax1.tail, true), ∀ buf1, m, x0, lax0, x1, lax1. # buf1 < #(buf2 + buf) → abs-nodes(buf1, m, x0, lax0, true) ∧ abs-nodes(buf1, m, x1, lax1, true) → x0 = x1 ∧ lax0 = lax1 ⊦ lax1 = [], x = x2 ∧ @(lax1.head.off, # buf2) ' + lax2 = lax1

Rule argument

Additional information

Used simplifier rules: ls-abs-node-buf-size: ⊦ abs-node(buf, nd) → # buf = nd.alignedsize + 2 * NODE_HEADER_SIZE;% ⊦ buf + buf0 = buf + buf1 ↔ buf0 = buf1; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ a ' + x = b ' + y ↔ a = b ∧ x = y; (ws)%⊦ abs-node(buf0, nd0) ∧ buf0 + buf2 = buf1 + buf3 → (abs-node(buf1, nd1) ↔ buf0 = buf1 ∧ nd0 = nd1); (s)% ⊦ abs-node(buf0, nd) ∧ buf0 + buf1 = buf + buf2 → ¬ abs-padding(buf); (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]