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Proof step 61 from proof truncate-empty (previous step)

VFS_PAGE_SIZE = n0 + n1, files1[ino0] = mkfile(m, md0, # links(ino0, dirs), content0), n0 ≠ 0, n1 ≠ 0, n1 < VFS_PAGE_SIZE, afs-cons(dirs, files1), ino0 ∈ files1, m0 ∈ content0 ⊦ [asynced := ?] ( ( ( (content0.stream to m0 * VFS_PAGE_SIZE + n1) + (σ⊥ to n0) + (content0.stream from VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE) from m0 * VFS_PAGE_SIZE + n1) to (VFS_PAGE_SIZE - n1)) + σ⊥ = σ⊥)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 62:
VFS_PAGE_SIZE = n0 + n1, VFS_PAGE_SIZE = n2 + n1, files1[ino0] = mkfile(m, md0, # links(ino0, dirs), content0), n1 < VFS_PAGE_SIZE, afs-cons(dirs, files1), m0 ∈ content0, ino0 ∈ files1, n1 ≤ VFS_PAGE_SIZE ⊦ [asynced := ?] ( ( ( (content0.stream to m0 * VFS_PAGE_SIZE + n1) + (σ⊥ to n0) + (content0.stream from VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE) from m0 * VFS_PAGE_SIZE + n1) to n2) + σ⊥ = σ⊥), n0 = 0, n1 = 0

Rule argument

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

Additional information

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