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Proof step 57 from proof truncate-inv (previous step)

⟨if n0 ≠ 0 ∧ m2 ∈ content0 then {pageno := m2; if buf-opt.some? then buf := buf-opt.buf else buf := files[ino4].content[pageno]; buf := fill(buf, zero, n0, VFS_PAGE_SIZE - n0); content[pageno] := buf; buf-opt := some(buf)}⟩ (pageno = pageno1 ∧ buf = buf0 ∧ content = content2 ∧ buf-opt = buf-opt0), ⟨afs_inode_sync#(mkinode(ino4, md, false, # links(ino4, dirs), 0, m2 * VFS_PAGE_SIZE + n0); dirs, files1)⟩ (dirs = dirs0 ∧ files1 = files0), files0[ino4] = mkfile(m, md0, m1, content1), files[ino4] = mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs), content0), buf-opt = none, content = content0, files1 = files[ino4, mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs), content2 upto (m2 * VFS_PAGE_SIZE + n0))], content1.stream from m2 * VFS_PAGE_SIZE + n0 ≠ σ⊥, n0 < VFS_PAGE_SIZE, afs-cons(dirs, files), afs-cons(dirs0, files0), files ~ files0, ino4 ∈ files ⊦

User applied rule call left

And obtained the following new goals

Proof step 58:
⟨let ino = inode.ino in if ino ∈ files then {files[ino].size := inode.size; files[ino].meta := inode.meta} else if ino ∈ dirs then dirs[ino].meta := inode.meta⟩ (dirs = dirs0 ∧ files = files0), ⟨if n0 ≠ 0 ∧ m2 ∈ content0 then {pageno := m2; if buf-opt.some? then buf := buf-opt.buf else buf := files2[ino4].content[pageno]; buf := fill(buf, zero, n0, VFS_PAGE_SIZE - n0); content[pageno] := buf; buf-opt := some(buf)}⟩ (pageno = pageno1 ∧ buf = buf0 ∧ content = content2 ∧ buf-opt = buf-opt0), files2[ino4] = mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs), content0), files0[ino4] = mkfile(m, md0, m1, content1), buf-opt = none, content = content0, files = files1, files1 = files2[ino4, mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs), content2 upto (m2 * VFS_PAGE_SIZE + n0))], inode = mkinode(ino4, md, false, # links(ino4, dirs), 0, m2 * VFS_PAGE_SIZE + n0), n0 < VFS_PAGE_SIZE, afs-cons(dirs0, files0), afs-cons(dirs, files2), files2 ~ files0, ino4 ∈ files2 ⊦ content1.stream from m2 * VFS_PAGE_SIZE + n0 = σ⊥

Rule argument

pos: left 2

Additional information

Used simplifier rules: afs_inode_sync#(INODE; DIRS, FILES) {let INO = INODE.ino in if INO ∈ FILES then {FILES[INO].size := INODE.size; FILES[INO].meta := INODE.meta} else if INO ∈ DIRS then DIRS[INO].meta := INODE.meta };