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Proof step 27 from proof abs-nodes-unique-weak-h (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 28:
⊦ 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 29:
abs-nodes(buf, m, x1, lax1, true), ∃ buf0, buf1. buf = buf0 + buf1 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf1, m + # buf0, nd ' + x, lax0, true) ∨ lax0 ≠ [] ∧ lax0.head.off = m ∧ lax0.head.size = # buf0 ∧ abs-node(buf0, nd) ∧ abs-nodes(buf1, m + # buf0, x, lax0.tail, true)), ∀ buf0, m, x0, lax0, x1, lax1. # buf0 < # buf → abs-nodes(buf0, m, x0, lax0, true) ∧ abs-nodes(buf0, m, x1, lax1, true) → 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] → [true, lax0, x, nd, m, buf] flags: <all paths>

Additional information

Used terms: true, lax0, x, nd, m, buf