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Proof step 39 from proof truncate-greater (previous step)

VFS_PAGE_SIZE = n0 + m3 % VFS_PAGE_SIZE, files0[m0] = mkfile(m, md0, # links(m0, dirs), content0), m3 % VFS_PAGE_SIZE ≠ 0, m3 < n, afs-cons(dirs, files0), m3 / VFS_PAGE_SIZE ∈ content0, m0 ∈ files0 ⊦ [asynced := ?] ( (content0[m3 / VFS_PAGE_SIZE, fill(content0[m3 / VFS_PAGE_SIZE], zero, m3 % VFS_PAGE_SIZE, n0)] upto m3).stream to n = (content0.stream to m3) + (σ⊥ to (n - m3)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 40:
VFS_PAGE_SIZE = n0 + m3 % VFS_PAGE_SIZE, files0[m0] = mkfile(m, md0, # links(m0, dirs), content0), n = n1 + m3, m3 < n, afs-cons(dirs, files0), m0 ∈ files0, m3 / VFS_PAGE_SIZE ∈ content0, m3 ≤ n ⊦ [asynced := ?] ( (content0[m3 / VFS_PAGE_SIZE, fill(content0[m3 / VFS_PAGE_SIZE], zero, m3 % VFS_PAGE_SIZE, n0)] upto m3).stream to n = (content0.stream to m3) + (σ⊥ to n1)), m3 % VFS_PAGE_SIZE = 0

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [m3, n, n1]

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n; (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: m3, n, n1