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Proof step 10 from proof abs-nodes-subarray-failed (previous step)

# buf0 = x0.flashsize, # buf1 = nd.alignedsize + 2 * NODE_HEADER_SIZE, lax.head.size = # buf1, n < # buf1 + x0.flashsize, abs-node(buf1, nd), abs-nodes(buf0, lax.head.off + # buf1, x0, lax.tail, false), is-aligned(n, 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)) ⊦ buf1 + buf0 = mkbuf(0), lax = [], n = 0, ∃ n0. n0 < # lax ∧ abs-nodes(subarray(buf1 + buf0, 0, n), lax.head.off, prefixn(n0, nd ' + x0), prefixn(n0, lax), true)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 11:
# buf1 = nd.alignedsize + 2 * NODE_HEADER_SIZE, # buf0 = x0.flashsize, ladr.size = # buf1, lax = ladr + lax0, n < # buf1 + x0.flashsize, abs-node(buf1, nd), abs-nodes(buf0, ladr.off + # buf1, x0, lax0, false), is-aligned(n, 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)) ⊦ buf1 + buf0 = mkbuf(0), lax = [], n = 0, ∃ n0. n0 < # lax ∧ abs-nodes(subarray(buf1 + buf0, 0, n), ladr.off, prefixn(n0, nd ' + x0), prefixn(n0, lax), true)

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: lax ≠ [] ⊦ ladr = lax.head ∧ lax0 = lax.tail ↔ lax = ladr + lax0; (elim) Used terms: lax, ladr, lax0