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Proof step 82 from proof truncate-inv (previous step)

files2[ino4] = mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content0), n0 < VFS_PAGE_SIZE, afs-cons(dirs0, files2), afs-cons (dirs0, files2 [ino4, mkfile (m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content0[m2, fill(content0[m2], zero, n0, VFS_PAGE_SIZE - n0)] upto (m2 * VFS_PAGE_SIZE + n0)) ]), files2 ~ files2 [ino4, mkfile (m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content0[m2, fill(content0[m2], zero, n0, VFS_PAGE_SIZE - n0)] upto (m2 * VFS_PAGE_SIZE + n0)) ], ino4 ∈ files2, m2 ∈ content0 ⊦ (content0[m2, fill(content0[m2], zero, n0, VFS_PAGE_SIZE - n0)].stream to VFS_PAGE_SIZE * m2 + VFS_PAGE_SIZE) + σ⊥ from m2 * VFS_PAGE_SIZE + n0 = σ⊥, n0 = 0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 83:
VFS_PAGE_SIZE = n1 + n0, files2[ino4] = mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content0), n0 < VFS_PAGE_SIZE, afs-cons (dirs0, files2 [ino4, mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content0[m2, fill(content0[m2], zero, n0, n1)] upto (m2 * VFS_PAGE_SIZE + n0)) ]), afs-cons(dirs0, files2), files2 ~ files2 [ino4, mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content0[m2, fill(content0[m2], zero, n0, n1)] upto (m2 * VFS_PAGE_SIZE + n0)) ], m2 ∈ content0, ino4 ∈ files2, n0 ≤ VFS_PAGE_SIZE ⊦ (content0[m2, fill(content0[m2], zero, n0, n1)].stream to VFS_PAGE_SIZE * m2 + VFS_PAGE_SIZE) + σ⊥ from m2 * VFS_PAGE_SIZE + n0 = σ⊥, n0 = 0

Rule argument

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

Additional information

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