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Proof step 55 from proof refine-read (previous step)

# buf2 = (n4 + n2) + n3, LEB_SIZE = n0 + n1, avols[default-volid][m2] = mapped(buf0, n1), n5 < n4 + n2, n3 < # buf2, m2 < # avols[default-volid], n5 < n2, ebm-cons(avols), ebm-vol-inv(abs(avols[default-volid])), default-volid ∈ avols, n2 + n3 ≤ # buf2, m1 + n2 ≤ LEB_SIZE, n3 + n2 ≤ # buf2, n1 ≤ LEB_SIZE ⊦ buf0[n5 + m1] = (subarray(buf0, 0, n1) + mkempbuf(n0))[m1 + n5]

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: array-splice, inst: buffer name: append-at seq: ⊦ n < # buf + # buf0 → (buf + buf0)[n] = (n < # buf ⊃ buf[n];buf0[n - # buf]) subst: [n, buf0, buf] → [m1 + n5, mkempbuf(n0), subarray(buf0, 0, n1)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # subarray(buf, m, n) = n; (s)% ⊦ # mkempbuf(n) = n; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)%c: ⊦ m + n = n + m; from specification nat-basic%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%⊦ v ∈ avols ∧ m < # avols[v] ∧ avols[v][m] = mapped(buf, m0) ∧ ebm-cons(avols) → # buf = LEB_SIZE; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%# buf = n ⊦ subarray(buf, 0, n) = buf; (s) Used terms: m1 + n5, mkempbuf(n0), subarray(buf0, 0, n1)