[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 68 from proof truncate-inv (previous step)

files2[ino4] = mkfile(m2 * VFS_PAGE_SIZE, md, # links(ino4, dirs0), content2), afs-cons(dirs0, files2), afs-cons(dirs0, files2[ino4, mkfile(m2 * VFS_PAGE_SIZE, md, # links(ino4, dirs0), content2 upto m2 * VFS_PAGE_SIZE)]), files2 ~ files2[ino4, mkfile(m2 * VFS_PAGE_SIZE, md, # links(ino4, dirs0), content2 upto m2 * VFS_PAGE_SIZE)], ino4 ∈ files2 ⊦ (content2 upto m2 * VFS_PAGE_SIZE).stream from m2 * VFS_PAGE_SIZE = σ⊥

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 69:
⊦ n = n0 * VFS_PAGE_SIZE → (content upto n).stream = (content.stream to n0 * VFS_PAGE_SIZE) + σ⊥
Proof step 70:
m2 * VFS_PAGE_SIZE = m2 * VFS_PAGE_SIZE, files2[ino4] = mkfile(m2 * VFS_PAGE_SIZE, md, # links(ino4, dirs0), content2), afs-cons(dirs0, files2[ino4, mkfile(m2 * VFS_PAGE_SIZE, md, # links(ino4, dirs0), content2 upto m2 * VFS_PAGE_SIZE)]), afs-cons(dirs0, files2), files2 ~ files2[ino4, mkfile(m2 * VFS_PAGE_SIZE, md, # links(ino4, dirs0), content2 upto m2 * VFS_PAGE_SIZE)], ino4 ∈ files2 ⊦ (content2.stream to m2 * VFS_PAGE_SIZE) + σ⊥ from m2 * VFS_PAGE_SIZE = σ⊥

Rule argument

spec: afs-stream name: content-trunc-exact seq: ⊦ n = n0 * VFS_PAGE_SIZE → (content upto n).stream = (content.stream to n0 * VFS_PAGE_SIZE) + σ⊥ subst: [n0, n, content] → [m2, m2 * VFS_PAGE_SIZE, content2] flags: <all paths>

Additional information

Used terms: m2, m2 * VFS_PAGE_SIZE, content2