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Proof step 25 from proof abs-nodes-split-h (previous step)

# buf1 = nd.alignedsize + 2 * NODE_HEADER_SIZE, abs-node(buf1, nd), abs-nodes(buf2, m + # buf1, x, lax0, false), abs-nodes(buf, (m + # buf1) + # buf2, x1, lax, weak), abs-nodes(buf2 + buf, m + # buf1, x + x1, lax0 + lax, weak), ∀ buf3, m, x0, x1, lax, weak. # buf3 < #(buf1 + buf2 + buf) → abs-nodes(buf3, m, x0 + x1, lax, weak) → (∃ buf4, buf1, lax0, lax1. lax = lax0 + lax1 ∧ buf3 = buf4 + buf1 ∧ abs-nodes(buf4, m, x0, lax0, false) ∧ abs-nodes(buf1, m + # buf4, x1, lax1, weak)) ⊦ abs-nodes(buf1 + buf2, m, nd ' + x, @(m, # buf1) ' + lax0, false)

User applied rule insert rewrite lemma

And obtained the following new goals

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] → [false, @(m, # buf1) ' + lax0, x, nd, m, buf1 + buf2] flags: <all paths>

Additional information

Used simplifier rules: append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ abs-node(buf0, nd) ∧ buf0 + buf1 = buf + buf2 → ¬ abs-padding(buf); (s)% ⊦ ladr ' + lax ≠ []; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]% ⊦ (ladr ' + lax).head = ladr; (s)% ⊦ @(m, m0).off = m; (s)% ⊦ @(m, m0).size = m0; (s)%⊦ abs-node(buf0, nd0) ∧ buf0 + buf2 = buf1 + buf3 → (abs-node(buf1, nd1) ↔ buf0 = buf1 ∧ nd0 = nd1); (s)% ⊦ (ladr ' + lax).tail = lax; (s)% ⊦ buf + buf0 = buf + buf1 ↔ buf0 = buf1; (s) Used terms: false, @(m, # buf1) ' + lax0, x, nd, m, buf1 + buf2