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Proof step 35 from proof range-eq-validtrailer (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
n0 < NODE_HEADER_SIZE, is-aligned(m, NODE_HEADER_SIZE), is-aligned(# buf, NODE_HEADER_SIZE), m + NODE_HEADER_SIZE ≤ # buf + n, m + NODE_HEADER_SIZE ≤ # buf, ∀ n1. n1 < NODE_HEADER_SIZE → buf[m + n1] = (validtrailer)[n1] ⊦ (buf + mkempbuf(n))[m + n0] = (validtrailer)[n0]

Rule argument

Additional information

Used simplifier rules: ⊦ NODE_HEADER_SIZE ≠ 0; (s)% ⊦ ¬ m + n < m; (s)% ⊦ NODE_HEADER_SIZE + n ≠ 0; (s)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ 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)