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Proof step 60 from proof refine-read (previous step)

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

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [n1, m1 + n5, n]

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%⊦ m0 + m1 < LEB_SIZE ∧ v ∈ avols ∧ m < # avols[v] ∧ avols[v][m] = mapped(buf, m0) ∧ ebm-cons(avols) → buf[m1 + m0] = empty; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m < n → n ≠ 0; (s)% ⊦ m < n → mkempbuf(n)[m] = empty; (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n1, m1 + n5, n