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Proof step 21 from proof abs-nodes-valid-node (previous step)

lax.head = @(m0, m1), is-encoded(nodeheader(m, boolvar0), subarray(buf, 0, NODE_HEADER_SIZE)), range=(buf, NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE), validtrailer, 0, NODE_HEADER_SIZE), 2 * NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE) ≤ # buf ⊦ (∃ buf0, buf1. buf = buf0 + buf1 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf1, n + # buf0, nd ' + x0, lax, weak) ∨ lax ≠ [] ∧ m0 = n ∧ m1 = # buf0 ∧ abs-node(buf0, nd) ∧ abs-nodes(buf1, n + # buf0, x0, lax.tail, weak))) ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ ( boolvar0 ∧ abs-padding(buf0) ∧ abs-nodes(buf1, n + # buf0, nd ' + x0, lax, weak) ∨ # buf0 = 2 * NODE_HEADER_SIZE + nd.alignedsize ∧ lax ≠ [] ∧ @(m0, m1) = @(n, # buf0) ∧ ¬ boolvar0 ∧ abs-node(buf0, nd) ∧ abs-nodes(buf1, n + # buf0, x0, lax.tail, weak)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 22:
ladr = @(m0, m1), lax = ladr + lax0, is-encoded(nodeheader(m, boolvar0), subarray(buf, 0, NODE_HEADER_SIZE)), range=(buf, NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE), validtrailer, 0, NODE_HEADER_SIZE), 2 * NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE) ≤ # buf ⊦ (∃ buf0, buf1. buf = buf0 + buf1 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf1, n + # buf0, nd ' + x0, lax, weak) ∨ lax ≠ [] ∧ m0 = n ∧ m1 = # buf0 ∧ abs-node(buf0, nd) ∧ abs-nodes(buf1, n + # buf0, x0, lax0, weak))) ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ ( boolvar0 ∧ abs-padding(buf0) ∧ abs-nodes(buf1, n + # buf0, nd ' + x0, lax, weak) ∨ # buf0 = 2 * NODE_HEADER_SIZE + nd.alignedsize ∧ lax ≠ [] ∧ @(m0, m1) = @(n, # buf0) ∧ ¬ boolvar0 ∧ abs-node(buf0, nd) ∧ abs-nodes(buf1, n + # buf0, x0, lax0, weak))), lax = []

Rule argument

spec: list-data, inst: laddress-list name: elim-list-c seq: lax ≠ [] ⊦ ladr = lax.head ∧ lax0 = lax.tail ↔ lax = ladr + lax0 subst: [lax, ladr, lax0] → [lax, ladr, lax0]

Additional information

Used simplifier rules: abs-nodes-first-adr-explicit: ⊦ abs-nodes(buf, m, a ' + x, lax, weak) → (lax.head = ladr ↔ (∃ lax0. lax = ladr + lax0));%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]%⊦ buf0 + buf1 = buf2 + buf3 ∧ abs-padding(buf0) → (abs-padding(buf2) ↔ buf0 = buf2); (s)% ⊦ buf + buf0 = buf + buf1 ↔ buf0 = buf1; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ ladr + lax = ladr ' + lax; (s)% ⊦ ladr ' + lax ≠ []; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]%lax ≠ [] ⊦ ladr = lax.head ∧ lax0 = lax.tail ↔ lax = ladr + lax0; (elim) Used terms: lax, ladr, lax0