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

abs-padding(buf2) ∧ abs-nodes(buf, m + # buf2, nd ' + x, lax0, false) ∨ lax0 ≠ [] ∧ lax0.head.off = m ∧ lax0.head.size = # buf2 ∧ abs-node(buf2, nd) ∧ abs-nodes(buf, lax0.head.off + # buf2, x, lax0.tail, false), ∀ buf3, m, x0, lax0, buf1, x1, lax1, weak. # buf3 < #(buf2 + buf) → abs-nodes(buf3, m, x0, lax0, false) → (abs-nodes(buf3 + buf1, m, x0 + x1, lax0 + lax1, weak) ↔ abs-nodes(buf1, m + # buf3, x1, lax1, weak)) ⊦ abs-nodes((buf2 + buf) + buf1, m, (nd ' + x) + x1, lax0 + lax1, weak) ↔ abs-nodes(buf1, m + # buf2 + # buf, x1, lax1, weak)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 15:
lax0.head = @(m0, m1), abs-padding(buf2) ∧ abs-nodes(buf, m + # buf2, nd ' + x, lax0, false) ∨ lax0 ≠ [] ∧ m0 = m ∧ m1 = # buf2 ∧ abs-node(buf2, nd) ∧ abs-nodes(buf, m0 + # buf2, x, lax0.tail, false), ∀ buf3, m, x0, lax0, buf1, x1, lax1, weak. # buf3 < #(buf2 + buf) → abs-nodes(buf3, m, x0, lax0, false) → (abs-nodes(buf3 + buf1, m, x0 + x1, lax0 + lax1, weak) ↔ abs-nodes(buf1, m + # buf3, x1, lax1, weak)) ⊦ abs-nodes((buf2 + buf) + buf1, m, (nd ' + x) + x1, lax0 + lax1, weak) ↔ abs-nodes(buf1, m + # buf2 + # buf, x1, lax1, weak)

Rule argument

spec: laddress name: elim seq: ⊦ m = ladr.off ∧ m0 = ladr.size ↔ ladr = @(m, m0) subst: [ladr, m, m0] → [lax0.head, m0, m1]

Additional information

Used simplifier rules: ⊦ m = ladr.off ∧ m0 = ladr.size ↔ ladr = @(m, m0); (elim) Used terms: lax0.head, m0, m1