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Proof step 7 from proof refine-get-leb-size (previous step)

m = EB_PAGE_SIZE, abs(pebs, apebs), mtd-cons(pebs), ubi-io-inv(apebs), PEB_SIZE ≥ 2 * m ⊦ ⟨aubi_io_get_leb_size#(apebs; ; n0)⟩ (PEB_SIZE - 2 * m = n0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
PEB_SIZE = n1 + 2 * m, m = EB_PAGE_SIZE, abs(pebs, apebs), mtd-cons(pebs), ubi-io-inv(apebs), 2 * m ≤ PEB_SIZE, PEB_SIZE ≥ 2 * m ⊦ ⟨aubi_io_get_leb_size#(apebs; ; n0)⟩ (n1 = n0)

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [PEB_SIZE, 2 * m, n]

Additional information

Used simplifier rules: ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ ¬ PEB_SIZE < 2 * EB_PAGE_SIZE; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: PEB_SIZE, 2 * m, n