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Proof step 19 from proof range-eq-validtrailer (previous step)

subarray(mkempbuf(n), n0, NODE_HEADER_SIZE) = validtrailer, is-aligned(# buf, NODE_HEADER_SIZE), is-aligned(n0, NODE_HEADER_SIZE), n0 + NODE_HEADER_SIZE ≤ n, 0 + NODE_HEADER_SIZE ≤ # validtrailer ⊦ n = 0, ∀ n. 0 ≤ n ∧ n < 0 + NODE_HEADER_SIZE → (validtrailer)[n] = empty

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
subarray(mkempbuf(n), n0, NODE_HEADER_SIZE) = validtrailer, n1 < NODE_HEADER_SIZE, is-aligned(# buf, NODE_HEADER_SIZE), is-aligned(n0, NODE_HEADER_SIZE), n0 + NODE_HEADER_SIZE ≤ n ⊦ (validtrailer)[n1] = empty, n = 0

Rule argument

Additional information

Used simplifier rules: ⊦ NODE_HEADER_SIZE ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ m; (s)% ⊦ # validtrailer = NODE_HEADER_SIZE; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ 0 ≤ m; (s)