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Proof step 5 from proof crash-neutral-truncate (previous step)

asynced, dirs0 = dirs \ orphans(dirs, files), files0 = files \ orphans(dirs, files), inode = mkinode(m, md, false, files[m].nlink, 0, m2), afs-cons(dirs, files), m ∈ files, buf-opt.some? → # buf-opt.buf = VFS_PAGE_SIZE ⊦ ⟨afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt, inode, asynced0, err, dirs, files, asynced)⟩ (asynced ∧ dirs0 = dirs \ orphans(dirs, files) ∧ files0 = files \ orphans(dirs, files))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
files[m] = mkfile(m0, md0, m1, content), asynced, dirs0 = dirs \ orphans(dirs, files), files0 = files \ orphans(dirs, files), inode = mkinode(m, md, false, m1, 0, m2), afs-cons(dirs, files), m ∈ files, buf-opt.some? → # buf-opt.buf = VFS_PAGE_SIZE ⊦ ⟨afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt, inode, asynced0, err, dirs, files, asynced)⟩ (asynced ∧ dirs0 = dirs \ orphans(dirs, files) ∧ files0 = files \ orphans(dirs, files))

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files[m], m0, md, m1, content]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files[m], m0, md, m1, content