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Proof step 11 from proof abs-nodes-append-h (previous step)

abs-nodes(buf0, m, nd ' + x, lax0, false), ∀ buf, m, x0, lax0, buf1, x1, lax1, weak. # buf < # buf0 → abs-nodes(buf, m, x0, lax0, false) → (abs-nodes(buf + buf1, m, x0 + x1, lax0 + lax1, weak) ↔ abs-nodes(buf1, m + # buf, x1, lax1, weak)) ⊦ abs-nodes(buf0 + buf1, m, (nd ' + x) + x1, lax0 + lax1, weak) ↔ abs-nodes(buf1, m + # buf0, x1, lax1, weak)

User applied rule insert rewrite lemma

And obtained the following new goals

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] → [false, lax0, x, nd, m, buf0] flags: <all paths>

Additional information

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