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Proof step 25 from proof range-eq-validtrailer (previous step)

mkempbuf(n)[n0 + n1] = (validtrailer)[n1], 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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: array-splice, inst: buffer name: emparray-at seq: ⊦ m < n → mkempbuf(n)[m] = empty subst: [m, n] → [n0 + n1, n] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: n0 + n1, n