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Proof step 9 from proof abs-nodes-subarray-failed (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
# 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)

Rule argument

Additional information

Used simplifier rules: size-rec: ⊦ (a ' + x).flashsize = a.flashsize + x.flashsize;%ls-abs-node-buf-size: ⊦ abs-node(buf, nd) → # buf = nd.alignedsize + 2 * NODE_HEADER_SIZE;% ⊦ m + n = m + n0 ↔ n = n0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ nd.flashsize = 2 * NODE_HEADER_SIZE + nd.alignedsize; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)