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Proof step 38 from proof range-eq-validtrailer (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 39:
m + n0 < # buf + n, n0 < NODE_HEADER_SIZE, is-aligned(# buf, NODE_HEADER_SIZE), is-aligned(m, NODE_HEADER_SIZE), m + NODE_HEADER_SIZE ≤ # buf, m + NODE_HEADER_SIZE ≤ # buf + n, ∀ n1. n1 < NODE_HEADER_SIZE → buf[m + n1] = (validtrailer)[n1] ⊦ buf[m + n0] = (validtrailer)[n0]

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < m + n ↔ n ≠ 0; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ # mkempbuf(n) = n; (s)