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Proof step 14 from proof abs-nodes-unique-weak-h (previous step)

abs-nodes(buf1, m + # buf0, [], [], true), abs-nodes(buf1, m + # buf0, nd ' + x2, lax1, true), abs-padding(buf0), ∀ buf2, m, x0, lax0, x1, lax1. # buf2 < #(buf0 + buf1) → abs-nodes(buf2, m, x0, lax0, true) ∧ abs-nodes(buf2, m, x1, lax1, true) → x0 = x1 ∧ lax0 = lax1 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ 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 16:
abs-nodes(buf1, m + # buf0, [], [], true), abs-padding(buf0), ∃ buf3, buf2. buf1 = buf3 + buf2 ∧ ( abs-padding(buf3) ∧ abs-nodes(buf2, (m + # buf0) + # buf3, nd ' + x2, lax1, true) ∨ lax1 ≠ [] ∧ lax1.head.off = m + # buf0 ∧ lax1.head.size = # buf3 ∧ abs-node(buf3, nd) ∧ abs-nodes(buf2, (m + # buf0) + # buf3, x2, lax1.tail, true)), ∀ buf2, m, x0, lax0, x1, lax1. # buf2 < #(buf0 + buf1) → abs-nodes(buf2, m, x0, lax0, true) ∧ abs-nodes(buf2, m, x1, lax1, true) → x0 = 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] → [true, lax1, x2, nd, m + # buf0, buf1] flags: <all paths>

Additional information

Used terms: true, lax1, x2, nd, m + # buf0, buf1