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Proof step 6 from proof abs-split-by-address-h (previous step)

abs-nodes(buf, m, nd ' + x2, lax0 + ladr ' + lax1, boolvar0), ∀ buf0, m, x, lax0, ladr, lax1, boolvar0. # buf0 < # buf → abs-nodes(buf0, m, x, lax0 + ladr ' + lax1, boolvar0) → (∃ buf3, buf1, buf2, x0, a, x1. x = x0 + a ' + x1 ∧ # x0 = # lax0 ∧ buf0 = buf3 + buf1 + buf2 ∧ ladr = @(m + # buf3, 2 * NODE_HEADER_SIZE + a.alignedsize) ∧ # buf1 = 2 * NODE_HEADER_SIZE + a.alignedsize ∧ abs-node(buf1, a)) ⊦ ∃ buf0, buf1, buf2, x, a, x0. nd ' + x2 = x + a ' + x0 ∧ # x = # lax0 ∧ buf = buf0 + buf1 + buf2 ∧ ladr = @(m + # buf0, 2 * NODE_HEADER_SIZE + a.alignedsize) ∧ # buf1 = 2 * NODE_HEADER_SIZE + a.alignedsize ∧ abs-node(buf1, a)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ 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 8:
∃ buf0, buf1. buf = buf0 + buf1 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf1, m + # buf0, nd ' + x2, lax0 + ladr ' + lax1, boolvar0) ∨ lax0 + ladr ' + lax1 ≠ [] ∧ (lax0 + ladr ' + lax1).head.off = m ∧ (lax0 + ladr ' + lax1).head.size = # buf0 ∧ abs-node(buf0, nd) ∧ abs-nodes(buf1, m + # buf0, x2, (lax0 + ladr ' + lax1).tail, boolvar0)), ∀ buf0, m, x, lax0, ladr, lax1, boolvar0. # buf0 < # buf → abs-nodes(buf0, m, x, lax0 + ladr ' + lax1, boolvar0) → (∃ buf3, buf1, buf2, x0, a, x1. x = x0 + a ' + x1 ∧ # x0 = # lax0 ∧ buf0 = buf3 + buf1 + buf2 ∧ ladr = @(m + # buf3, 2 * NODE_HEADER_SIZE + a.alignedsize) ∧ # buf1 = 2 * NODE_HEADER_SIZE + a.alignedsize ∧ abs-node(buf1, a)) ⊦ ∃ buf0, buf1, buf2, x, a, x0. nd ' + x2 = x + a ' + x0 ∧ # x = # lax0 ∧ buf = buf0 + buf1 + buf2 ∧ ladr = @(m + # buf0, 2 * NODE_HEADER_SIZE + a.alignedsize) ∧ # buf1 = 2 * NODE_HEADER_SIZE + a.alignedsize ∧ abs-node(buf1, a)

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] → [boolvar0, lax0 + ladr ' + lax1, x2, nd, m, buf] flags: <all paths>

Additional information

Used terms: boolvar0, lax0 + ladr ' + lax1, x2, nd, m, buf