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Proof step 45 from proof abs-nodes-subarray-failed (previous step)

# buf1 = nd.alignedsize + 2 * NODE_HEADER_SIZE, # buf0 = x0.flashsize, n1 < x0.flashsize, n < # lax0, abs-node(buf1, nd), abs-nodes(buf0, m0 + # buf1, x0, lax0, false), abs-nodes(subarray(buf0, 0, n1), m0 + # buf1, prefixn(n, x0), prefixn(n, lax0), true), is-aligned(n1, NODE_HEADER_SIZE), ∀ buf2, x, n, m, lax. # buf2 < #(buf1 + buf0) → # buf2 = x.flashsize ∧ n < x.flashsize ∧ abs-nodes(buf2, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) → n = 0 ∨ x = [] ∨ (∃ n0. n0 < # lax ∧ abs-nodes(subarray(buf2, 0, n), m, prefixn(n0, x), prefixn(n0, lax), true)) ⊦ n1 + # buf1 = 0, buf1 + buf0 = mkbuf(0), lax0 = [], x0 = [], abs-nodes(buf1 + subarray(buf0, 0, n1), m0, nd ' + prefixn(n, x0), @(m0, # buf1) ' + prefixn(n, lax0), true)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 46:
⊦ 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] → [true, @(m0, # buf1) ' + prefixn(n, lax0), prefixn(n, x0), nd, m0, buf1 + subarray(buf0, 0, n1)] 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: true, @(m0, # buf1) ' + prefixn(n, lax0), prefixn(n, x0), nd, m0, buf1 + subarray(buf0, 0, n1)