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Proof step 38 from proof abs-nodes-append-h (previous step)

# buf2 = nd.alignedsize + 2 * NODE_HEADER_SIZE, (buf2 + buf) + buf1 = buf0 + buf3, abs-node(buf2, nd), abs-nodes(buf3, m + # buf0, nd ' + x + x1, (@(m, # buf2) ' + lax2) + lax1, weak), abs-nodes(buf, m + # buf2, x, lax2, false), abs-padding(buf0), ∀ 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(buf + buf1, m + # buf2, x + x1, lax2 + lax1, weak), abs-nodes(buf1, (m + # buf2) + # buf, x1, lax1, weak)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: abs-node name: abs-node-no-abs-padding seq: ⊦ abs-node(buf0, nd) ∧ buf0 + buf1 = buf + buf2 → ¬ abs-padding(buf) subst: [buf0, nd, buf1, buf2, buf] → [buf2, nd, buf + buf1, buf3, buf0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ abs-node(buf, nd0) → (abs-node(buf, nd1) ↔ nd0 = nd1); (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer] Used terms: buf2, nd, buf + buf1, buf3, buf0