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Proof step 54 from proof truncate-same-iso (previous step)

VFS_PAGE_SIZE = n0 + m % VFS_PAGE_SIZE, files0[ino0] = mkfile(m, md, # links(ino0, dirs), content), afs-cons(dirs, files0), m / VFS_PAGE_SIZE ∈ content, ino0 ∈ files0 ⊦ m % VFS_PAGE_SIZE = 0, content.stream to m = (content.stream to m / VFS_PAGE_SIZE * VFS_PAGE_SIZE) + (((content.stream from m / VFS_PAGE_SIZE * VFS_PAGE_SIZE) to VFS_PAGE_SIZE to m % VFS_PAGE_SIZE) + (σ⊥ to n0)) + (content.stream from VFS_PAGE_SIZE * m / VFS_PAGE_SIZE + VFS_PAGE_SIZE) to m

User applied rule insert elim lemma

And obtained the following new goals

Proof step 55:
VFS_PAGE_SIZE = n0 + n1, files0[ino0] = mkfile(m, md, # links(ino0, dirs), content), m = m0 * VFS_PAGE_SIZE + n1, n1 < VFS_PAGE_SIZE, afs-cons(dirs, files0), ino0 ∈ files0, m0 ∈ content ⊦ VFS_PAGE_SIZE = 0, n1 = 0, content.stream to m = (content.stream to m0 * VFS_PAGE_SIZE) + (((content.stream from m0 * VFS_PAGE_SIZE) to VFS_PAGE_SIZE to n1) + (σ⊥ to n0)) + (content.stream from VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE) to m

Rule argument

spec: nat-div name: div-elim seq: n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n subst: [n, m, m0, n0] → [VFS_PAGE_SIZE, m, m0, n]

Additional information

Used simplifier rules: ⊦ VFS_PAGE_SIZE ≠ 0; (s)%n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n; (elim) Used terms: VFS_PAGE_SIZE, m, m0, n