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Proof step 8 from proof abs-nodes-case-distinction-h (previous step)

abs-nodes(buf, m, nd ' + x0, lax, true) ⊦ ∃ buf0, buf1. buf = buf0 + buf1 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf1, m + # buf0, nd ' + x0, lax, true) ∨ lax ≠ [] ∧ (∃ lax0. lax = @(m, 2 * NODE_HEADER_SIZE + nd.alignedsize) ' + lax0) ∧ abs-node(buf0, nd) ∧ abs-nodes(buf1, m + # buf0, x0, lax.tail, true))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ 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 10:
∃ buf0, buf1. buf = buf0 + buf1 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf1, m + # buf0, nd ' + x0, lax, true) ∨ lax ≠ [] ∧ lax.head.off = m ∧ lax.head.size = # buf0 ∧ abs-node(buf0, nd) ∧ abs-nodes(buf1, m + # buf0, x0, lax.tail, true)) ⊦ ∃ buf0, buf1. buf = buf0 + buf1 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf1, m + # buf0, nd ' + x0, lax, true) ∨ lax ≠ [] ∧ (∃ lax0. lax = @(m, 2 * NODE_HEADER_SIZE + nd.alignedsize) ' + lax0) ∧ abs-node(buf0, nd) ∧ abs-nodes(buf1, m + # buf0, x0, lax.tail, true))

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, lax, x0, nd, m, buf] flags: <all paths>

Additional information

Used terms: true, lax, x0, nd, m, buf