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Proof step 22 from proof abs-nodes-subarray-failed (previous step)

# buf1 = nd.alignedsize + 2 * NODE_HEADER_SIZE, # buf0 = x0.flashsize, n < # buf1 + x0.flashsize, abs-node(buf1, nd), abs-nodes(buf0, m0 + # buf1, x0, lax0, false), is-aligned(n, NODE_HEADER_SIZE), # buf1 ≤ n, ∀ 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), n = 0, x0 = [], ∃ n0. ¬ # lax0 < n0 ∧ abs-nodes(buf1 + subarray(buf0, 0, n - # buf1), m0, prefixn(n0, nd ' + x0), prefixn(n0, @(m0, # buf1) ' + lax0), true)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 23:
# buf0 = x0.flashsize, # buf1 = nd.alignedsize + 2 * NODE_HEADER_SIZE, n = n1 + # buf1, n < # buf1 + x0.flashsize, abs-node(buf1, nd), abs-nodes(buf0, m0 + # buf1, x0, lax0, false), is-aligned(n, NODE_HEADER_SIZE), # buf1 ≤ n, ∀ 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), n = 0, x0 = [], ∃ n0. ¬ # lax0 < n0 ∧ abs-nodes(buf1 + subarray(buf0, 0, n1), m0, prefixn(n0, nd ' + x0), prefixn(n0, @(m0, # buf1) ' + lax0), true)

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [n, # buf1, n1]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n, # buf1, n1