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Proof step 26 from proof abs-nodes-prefix-h (previous step)

# buf2 = nd.alignedsize + 2 * NODE_HEADER_SIZE, abs-node(buf2, nd), abs-nodes(buf, m + # buf2, x, lax2, boolvar0), abs-nodes((buf2 + buf) + buf1, m, nd0 ' + x2, lax1, boolvar1), ∀ buf3, buf1, m, x1, lax1, boolvar1, x0, lax0, boolvar0. # buf3 < #(buf2 + buf) → abs-nodes(buf3 + buf1, m, x1, lax1, boolvar1) ∧ abs-nodes(buf3, m, x0, lax0, boolvar0) → x0 ⊑ x1 ∧ lax0 ⊑ lax1 ⊦ nd ' + x ⊑ nd0 ' + x2 ∧ @(m, # buf2) ' + lax2 ⊑ lax1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 27:
⊦ abs-nodes(buf, m, a ' + x, lax, weak) ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf1, m + # buf0, a ' + x, lax, weak) ∨ lax ≠ [] ∧ lax.head.off = m ∧ lax.head.size = # buf0 ∧ abs-node(buf0, a) ∧ abs-nodes(buf1, m + # buf0, x, lax.tail, weak)))
Proof step 28:
# buf2 = nd.alignedsize + 2 * NODE_HEADER_SIZE, abs-node(buf2, nd), abs-nodes(buf, m + # buf2, x, lax2, boolvar0), ∃ buf0, buf3. (buf2 + buf) + buf1 = buf0 + buf3 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf3, m + # buf0, nd0 ' + x2, lax1, boolvar1) ∨ lax1 ≠ [] ∧ lax1.head.off = m ∧ lax1.head.size = # buf0 ∧ abs-node(buf0, nd0) ∧ abs-nodes(buf3, m + # buf0, x2, lax1.tail, boolvar1)), ∀ buf3, buf1, m, x1, lax1, boolvar1, x0, lax0, boolvar0. # buf3 < #(buf2 + buf) → abs-nodes(buf3 + buf1, m, x1, lax1, boolvar1) ∧ abs-nodes(buf3, m, x0, lax0, boolvar0) → x0 ⊑ x1 ∧ lax0 ⊑ lax1 ⊦ nd ' + x ⊑ nd0 ' + x2 ∧ @(m, # buf2) ' + lax2 ⊑ lax1

Rule argument

spec: <toplevel> name: abs-nodes-rec seq: ⊦ abs-nodes(buf, m, a ' + x, lax, weak) ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf1, m + # buf0, a ' + x, lax, weak) ∨ lax ≠ [] ∧ lax.head.off = m ∧ lax.head.size = # buf0 ∧ abs-node(buf0, a) ∧ abs-nodes(buf1, m + # buf0, x, lax.tail, weak))) subst: [weak, lax, x, a, m, buf] → [boolvar1, lax1, x2, nd0, m, (buf2 + buf) + buf1] flags: <all paths>

Additional information

Used terms: boolvar1, lax1, x2, nd0, m, (buf2 + buf) + buf1