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Proof step 29 from proof abs-nodes-unique-strong-h (previous step)

# buf1 = nd.alignedsize + 2 * NODE_HEADER_SIZE, abs-node(buf1, nd), abs-nodes(buf0, m + # buf1, x, lax2, false), ∀ buf2, m, x0, lax0, x1, lax1, boolvar1. # buf2 < #(buf1 + buf0) → abs-nodes(buf2, m, x0, lax0, false) → (abs-nodes(buf2, m, x1, lax1, boolvar1) ↔ x0 = x1 ∧ lax0 = lax1) ⊦ (∃ buf3, buf2. buf1 + buf0 = buf3 + buf2 ∧ ( abs-padding(buf3) ∧ abs-nodes(buf2, m + # buf3, nd0 ' + x2, lax1, boolvar1) ∨ lax1 ≠ [] ∧ lax1.head.off = m ∧ lax1.head.size = # buf3 ∧ abs-node(buf3, nd0) ∧ abs-nodes(buf2, m + # buf3, x2, lax1.tail, boolvar1))) ↔ nd ' + x = nd0 ' + x2 ∧ @(m, # buf1) ' + lax2 = lax1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 30:
# buf1 = nd.alignedsize + 2 * NODE_HEADER_SIZE, abs-node(buf1, nd), abs-nodes(buf0, m + # buf1, x, lax2, false), ∀ buf2, m, x0, lax0, x1, lax1, boolvar1. # buf2 < #(buf1 + buf0) → abs-nodes(buf2, m, x0, lax0, false) → (abs-nodes(buf2, m, x1, lax1, boolvar1) ↔ x0 = x1 ∧ lax0 = lax1) ⊦ lax1 ≠ [] ∧ lax1.head.off = m ∧ lax1.head.size = # buf1 ∧ nd = nd0 ∧ abs-nodes(buf0, lax1.head.off + # buf1, x2, lax1.tail, boolvar1) ↔ nd ' + x = nd0 ' + x2 ∧ @(m, # buf1) ' + lax2 = lax1

Rule argument

Additional information

Used simplifier rules: ⊦ buf + buf0 = buf + buf1 ↔ buf0 = buf1; (s)%⊦ 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]