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Proof step 7 from proof abs-nodes-prefix-h (previous step)

abs-nodes(buf0 + buf1, m, x1, lax1, boolvar1), abs-nodes(buf0, m, nd ' + x, lax0, boolvar0), ∀ buf, buf1, m, x1, lax1, boolvar1, x0, lax0, boolvar0. # buf < # buf0 → abs-nodes(buf + buf1, m, x1, lax1, boolvar1) ∧ abs-nodes(buf, m, x0, lax0, boolvar0) → x0 ⊑ x1 ∧ lax0 ⊑ lax1 ⊦ nd ' + x ⊑ x1 ∧ lax0 ⊑ lax1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ 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 9:
abs-nodes(buf0 + buf1, m, x1, lax1, boolvar1), ∃ buf2, buf1. buf0 = buf2 + buf1 ∧ ( abs-padding(buf2) ∧ abs-nodes(buf1, m + # buf2, nd ' + x, lax0, boolvar0) ∨ lax0 ≠ [] ∧ lax0.head.off = m ∧ lax0.head.size = # buf2 ∧ abs-node(buf2, nd) ∧ abs-nodes(buf1, m + # buf2, x, lax0.tail, boolvar0)), ∀ buf, buf1, m, x1, lax1, boolvar1, x0, lax0, boolvar0. # buf < # buf0 → abs-nodes(buf + buf1, m, x1, lax1, boolvar1) ∧ abs-nodes(buf, m, x0, lax0, boolvar0) → x0 ⊑ x1 ∧ lax0 ⊑ lax1 ⊦ nd ' + x ⊑ x1 ∧ lax0 ⊑ 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] → [boolvar0, lax0, x, nd, m, buf0] flags: <all paths>

Additional information

Used terms: boolvar0, lax0, x, nd, m, buf0