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Proof step 33 from proof truncate-inv (previous step)

⟨ let ino = inode.ino, content = files[inode.ino].content, buf = ? in {ino1 := inode.size % VFS_PAGE_SIZE, ino0 := min(n, inode.size); isdir := inode.size ≤ n ∧ ino1 ≠ 0 ∧ (pageno ∈ content ∨ buf-opt.some?); if isdir then {if buf-opt.some? then buf := buf-opt.buf else buf := files[ino].content[pageno]; buf := fill(buf, zero, ino1, VFS_PAGE_SIZE - ino1); content[pageno] := buf; buf-opt := some(buf)}; files[ino].content := content upto ino0; let new_inode = inode in {new_inode.size := n; afs_inode_sync#(new_inode; dirs, files)}; inode := getinode(inode.ino, dirs, files); err := ESUCCESS} or fail#(; ; err)⟩ (ino1 = ino6 ∧ ino0 = ino7 ∧ (isdir ↔ isdir1) ∧ buf-opt = buf-opt0 ∧ files = files2 ∧ dirs = dirs1 ∧ inode = inode1 ∧ err = err1), isdir1 ↔ isdir0, asynced ↔ asynced1, files1[ino4] = mkfile(m0, md, # links(ino4, dirs), content0), buf-opt = none, buf-opt0 = buf-opt1, dirs1 = dirs0, err1 = err0, files = files1, files2 = files0, ino = 0, ino0 = ino, ino1 = ino5, ino5 = 0, ino6 = ino2, ino7 = ino3, inode = mkinode(ino4, md, false, # links(ino4, dirs), 0, m0), inode1 = inode0, n = m0, pageno = m0 / VFS_PAGE_SIZE, afs-cons(dirs, files1), afs-cons(dirs0, files0), files1 ~ files0, ino4 ∈ files1, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ VFS_PAGE_SIZE = 0, (err0 = ESUCCESS ⊃ files0[ino4].content.stream from m0 = σ⊥ ∧ (n0 ≤ # buf → ino4 ∈ files0 ∧ files0[ino4].size = m0) ∧ files1 -- ino4 = files0 -- ino4 ;⌊err0⌋ ) ∧ inode0 = mkinode(ino4, md, false, # links(ino4, dirs), 0, m0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 34:
⟨ 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 = ino6 ∧ ino0 = ino7 ∧ (isdir ↔ isdir1) ∧ buf-opt = buf-opt0 ∧ files1 = files0 ∧ dirs = dirs0 ∧ inode = inode0 ∧ err = err0), 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(dirs0, files0), afs-cons(dirs, files1), files1 ~ files0, ino4 ∈ files1, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ (err0 = ESUCCESS ⊃ files0[ino4].content.stream from m0 = σ⊥ ∧ (n0 ≤ # buf → ino4 ∈ files0 ∧ files0[ino4].size = m0) ∧ files1 -- ino4 = files0 -- ino4 ;⌊err0⌋ ) ∧ inode0 = mkinode(ino4, md, false, # links(ino4, dirs), 0, m0)

Rule argument

Additional information

Used simplifier rules: ⊦ VFS_PAGE_SIZE ≠ 0; (s)