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Proof step 16 from proof abs-nodes-case-distinction-h (previous step)

lax.head = @(m0, m1), m0 = m, m1 = # buf1, abs-node(buf1, nd), abs-nodes(buf0, m + # buf1, x0, lax.tail, true) ⊦ lax = [], ∃ buf3, buf2. buf1 + buf0 = buf3 + buf2 ∧ ( abs-padding(buf3) ∧ abs-nodes(buf2, m + # buf3, nd ' + x0, lax, true) ∨ lax ≠ [] ∧ (∃ lax0. lax = @(m, 2 * NODE_HEADER_SIZE + nd.alignedsize) ' + lax0) ∧ abs-node(buf3, nd) ∧ abs-nodes(buf2, m + # buf3, x0, lax.tail, true))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
# buf1 = nd.alignedsize + 2 * NODE_HEADER_SIZE, lax.head = @(m, # buf1), abs-node(buf1, nd), abs-nodes(buf0, m + # buf1, x0, lax.tail, true) ⊦ lax = [], ∃ lax0. lax = @(m, # buf1) ' + lax0

Rule argument

Additional information

Used simplifier rules: abs-nodes-unique-weak-h: ⊦ abs-nodes(buf, m, x0, lax0, true) → (abs-nodes(buf, m, x1, lax1, true) ↔ x0 = x1 ∧ lax0 = lax1);%ls-abs-node-buf-size: ⊦ abs-node(buf, nd) → # buf = nd.alignedsize + 2 * NODE_HEADER_SIZE;%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ 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]