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Proof step 4 from proof abs-nodes-first-adr-explicit (previous step)

abs-nodes(buf, m, a ' + x, lax, weak), ∀ buf0, m, a, x, lax, weak. # buf0 < # buf → abs-nodes(buf0, m, a ' + x, lax, weak) → (∃ lax0. lax = lax.head ' + lax0) ⊦ ∃ lax0. lax = lax.head ' + lax0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 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 6:
∃ 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)), ∀ buf0, m, a, x, lax, weak. # buf0 < # buf → abs-nodes(buf0, m, a ' + x, lax, weak) → (∃ lax0. lax = lax.head ' + lax0) ⊦ ∃ lax0. lax = lax.head ' + lax0

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] → [weak, lax, x, a, m, buf] flags: <all paths>

Additional information

Used terms: weak, lax, x, a, m, buf