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Proof step 95 from proof truncate-greater (previous step)

files1[m0] = mkfile(m, md0, # links(m0, dirs), content0), m3 < n, afs-cons(dirs, files1), m0 ∈ files1 ⊦ [asynced := ?] ((content0 upto m3).stream to n = (content0.stream to m3) + (σ⊥ to (n - m3))), m3 % VFS_PAGE_SIZE ≠ 0 ∧ m3 / VFS_PAGE_SIZE ∈ content0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 96:
files1[m0] = mkfile(m, md0, # links(m0, dirs), content0), n = n0 + m3, m3 < n, afs-cons(dirs, files1), m0 ∈ files1, m3 ≤ n ⊦ [asynced := ?] ((content0 upto m3).stream to n = (content0.stream to m3) + (σ⊥ to n0)), m3 % VFS_PAGE_SIZE ≠ 0 ∧ m3 / VFS_PAGE_SIZE ∈ content0

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [m3, n, n0]

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n; (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: m3, n, n0