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Proof step 42 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), x0 = [], ∃ n0. ¬ # lax0 < n0 ∧ abs-nodes(buf1 + subarray(buf0, 0, n1), m0, prefixn(n0, nd ' + x0), prefixn(n0, @(m0, # buf1) ' + lax0), true)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 43:
# 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 = [], ∃ n0. ¬ # lax0 < n0 ∧ abs-nodes(buf1 + subarray(buf0, 0, n1), m0, prefixn(n0, nd ' + x0), prefixn(n0, @(m0, # buf1) ' + lax0), true)

Rule argument

Additional information

Used simplifier rules: ⊦ # lax = 0 ↔ lax = []; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic