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Proof step 29 from proof abs-nodes-no-padding-last (previous step)

# buf = a.alignedsize + 2 * NODE_HEADER_SIZE, # buf1 = a0.alignedsize + 2 * NODE_HEADER_SIZE, # buf2 + # buf = (x0 + a ').flashsize, abs-node(buf1, a0), abs-node(buf, a), abs-nodes(buf2 + buf, m0 + # buf1, x0 + a ', lax1 + @(# buf2 + m0 + # buf1, # buf) ', false), abs-nodes(buf2, m0 + # buf1, x0, lax1, false), ∀ buf3, x, a, m, lax, ladr. # buf3 < #(buf1 + buf2 + buf) → # buf3 = (x + a ').flashsize ∧ abs-nodes(buf3, m, x + a ', lax + ladr ', false) → (∃ buf4, buf1. buf3 = buf4 + buf1 ∧ abs-nodes(buf4, m, x, lax, false) ∧ abs-node(buf1, a) ∧ ladr = @(# buf4 + m, 2 * NODE_HEADER_SIZE + a.alignedsize)) ⊦ abs-nodes(buf1 + buf2, m0, a0 ' + x0, @(m0, # buf1) ' + lax1, false)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 30:
⊦ 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)))

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, @(m0, # buf1) ' + lax1, x0, a0, m0, 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, @(m0, # buf1) ' + lax1, x0, a0, m0, buf1 + buf2