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Proof step 39 from proof truncate-inv (previous step)

⟨ let ino2 = inode.ino, content = files1[inode.ino].content, buf = ? in {ino := inode.size % VFS_PAGE_SIZE, ino0 := min(m0, inode.size); isdir := inode.size ≤ m0 ∧ ino ≠ 0 ∧ (m0 / VFS_PAGE_SIZE ∈ content ∨ buf-opt.some?); if isdir then {pageno := m0 / VFS_PAGE_SIZE; if buf-opt.some? then buf := buf-opt.buf else buf := files1[ino2].content[pageno]; buf := fill(buf, zero, ino, VFS_PAGE_SIZE - ino); content[pageno] := buf; buf-opt := some(buf)}; files1[ino2].content := content upto ino0; let new_inode = inode in {new_inode.size := m0; afs_inode_sync#(new_inode; dirs, files1)}; inode := getinode(inode.ino, dirs, files1); err := ESUCCESS} or fail#(; ; err)⟩ ( ino = ino1 ∧ ino0 = ino3 ∧ (isdir ↔ isdir0) ∧ pageno = pageno0 ∧ buf-opt = buf-opt1 ∧ files1 = files0 ∧ dirs = dirs0 ∧ inode = inode0 ∧ err = ESUCCESS), files1[ino4] = mkfile(m0, md, # links(ino4, dirs), content0), buf-opt = none, ino = 0, ino0 = 0, inode = mkinode(ino4, md, false, # links(ino4, dirs), 0, m0), afs-cons(dirs, files1), afs-cons(dirs0, files0), files1 ~ files0, ino4 ∈ files1 ⊦ files0[ino4].content.stream from m0 = σ⊥ ∧ (n0 ≤ # buf → ino4 ∈ files0 ∧ files0[ino4].size = m0) ∧ files1 -- ino4 = files0 -- ino4

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 40:
⟨ let ino2 = inode.ino, content = files1[inode.ino].content, buf = ? in {ino := inode.size % VFS_PAGE_SIZE, ino0 := min(m0, inode.size); isdir := inode.size ≤ m0 ∧ ino ≠ 0 ∧ (m0 / VFS_PAGE_SIZE ∈ content ∨ buf-opt.some?); if isdir then {pageno := m0 / VFS_PAGE_SIZE; if buf-opt.some? then buf := buf-opt.buf else buf := files1[ino2].content[pageno]; buf := fill(buf, zero, ino, VFS_PAGE_SIZE - ino); content[pageno] := buf; buf-opt := some(buf)}; files1[ino2].content := content upto ino0; let new_inode = inode in {new_inode.size := m0; afs_inode_sync#(new_inode; dirs, files1)}; inode := getinode(inode.ino, dirs, files1); err := ESUCCESS} or fail#(; ; err)⟩ ( ino = ino1 ∧ ino0 = ino3 ∧ (isdir ↔ isdir0) ∧ pageno = pageno0 ∧ buf-opt = buf-opt1 ∧ files1 = files0 ∧ dirs = dirs0 ∧ inode = inode0 ∧ err = ESUCCESS), files1[ino4] = mkfile(m0, md, # links(ino4, dirs), content0), files0[ino4] = mkfile(m, md0, m1, content1), buf-opt = none, ino = 0, ino0 = 0, inode = mkinode(ino4, md, false, # links(ino4, dirs), 0, m0), afs-cons(dirs0, files0), afs-cons(dirs, files1), files1 ~ files0, ino4 ∈ files1 ⊦ content1.stream from m0 = σ⊥ ∧ (n0 ≤ # buf → ino4 ∈ files0 ∧ m = m0) ∧ files1 -- ino4 = files0 -- ino4

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] → [files0[ino4], m, md0, m1, content1]

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: files0[ino4], m, md0, m1, content1