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Proof step 235 from proof inv-write (previous step)

m5 + n1 = m5 / VFS_PAGE_SIZE * VFS_PAGE_SIZE + VFS_PAGE_SIZE, of[fd] = mkfile(m, mode, m0), files1[m] = mkfile(m5, md, # links(m, dirs), content0), dirs1 = dirs, err0 = ESUCCESS, m5 = n2 + m5 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, ino4 ≠ 0, n ≠ 0, n2 ≠ 0, dom of < ino3, m5 < m0 + ino4, afs-cons(dirs, files), afs-cons(dirs, files1), of-cons(of, dirs, files), of-cons(of, dirs, files1), m ∈ files1, m5 / VFS_PAGE_SIZE ∈ content0, fd ∈ of, m5 % VFS_PAGE_SIZE + n1 ≤ VFS_PAGE_SIZE, n ≤ # buf0, n2 + n1 ≤ VFS_PAGE_SIZE ⊦ [afs_write_inode# (mkinode (m, files1 [m, files1 [m, files1 [m, mkfile (m5, md, # links(m, dirs), content0[m5 / VFS_PAGE_SIZE, fill(content0[m5 / VFS_PAGE_SIZE], zero, m5 % VFS_PAGE_SIZE, n1)] upto m5) ] [m ] .size:= m5 ] [m ] .meta:= md ] [m ] .meta, false, files1 [m, files1 [m, files1 [m, mkfile (m5, md, # links(m, dirs), content0[m5 / VFS_PAGE_SIZE, fill(content0[m5 / VFS_PAGE_SIZE], zero, m5 % VFS_PAGE_SIZE, n1)] upto m5) ] [m ] .size:= m5 ] [m ] .meta:= md ] [m ] .nlink, 0, m0 + ino4) ; err0, dirs, files ; asynced); if err0 ≠ ESUCCESS then ino4 := (m0 ≤ m5 ⊃ m5 - m0;0), err0 := ESUCCESS; of[fd].pos := m0 + ino4] (dirs1 = dirs → of-cons(of, dirs, files) ∧ dom of < ino3 ∧ afs-cons(dirs, files)), err1 = ESUCCESS ∧ ¬ isdir, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 236:
m5 + n1 = m5 / VFS_PAGE_SIZE * VFS_PAGE_SIZE + VFS_PAGE_SIZE, files1[m] = mkfile(m5, md, # links(m, dirs), content0), of[fd] = mkfile(m, mode, m0), files1 [m, files1 [m, files1 [m, mkfile (m5, md, # links(m, dirs), content0[m5 / VFS_PAGE_SIZE, fill(content0[m5 / VFS_PAGE_SIZE], zero, m5 % VFS_PAGE_SIZE, n1)] upto m5) ] [m ] .size:= m5 ] [m ] .meta:= md ] [m ] = mkfile(m1, md0, m2, content), dirs1 = dirs, err0 = ESUCCESS, m5 = n2 + m5 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, m5 < m0 + ino4, dom of < ino3, afs-cons(dirs, files1), afs-cons(dirs, files), of-cons(of, dirs, files1), of-cons(of, dirs, files), fd ∈ of, m5 / VFS_PAGE_SIZE ∈ content0, m ∈ files1, n2 + n1 ≤ VFS_PAGE_SIZE, n ≤ # buf0, m5 % VFS_PAGE_SIZE + n1 ≤ VFS_PAGE_SIZE ⊦ [afs_write_inode#(mkinode(m, md0, false, m2, 0, m0 + ino4); err0, dirs, files; asynced); if err0 ≠ ESUCCESS then ino4 := (m0 ≤ m5 ⊃ m5 - m0;0), err0 := ESUCCESS; of[fd].pos := m0 + ino4] (dirs1 = dirs → of-cons(of, dirs, files) ∧ dom of < ino3 ∧ afs-cons(dirs, files)), ino4 = 0, n = 0, n2 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW, err1 = ESUCCESS ∧ ¬ isdir

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] → [files1 [m, files1 [m, files1 [m, mkfile (m5, md, # links(m, dirs), content0 [m5 / VFS_PAGE_SIZE, fill (content0[m5 / VFS_PAGE_SIZE], zero, m5 % VFS_PAGE_SIZE, n1) ] upto m5) ] [m ] .size:= m5 ] [m ] .meta:= md ] [m ], m1, md0, m2, 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: files1 [m, files1 [m, files1 [m, mkfile (m5, md, # links(m, dirs), content0 [m5 / VFS_PAGE_SIZE, fill (content0[m5 / VFS_PAGE_SIZE], zero, m5 % VFS_PAGE_SIZE, n1) ] upto m5) ] [m ] .size:= m5 ] [m ] .meta:= md ] [m ], m1, md0, m2, content