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Proof step 102 from proof write-term (previous step)

VFS_PAGE_SIZE = n1 + m5 % VFS_PAGE_SIZE, files[m] = mkfile(m1, md, # links(m, dirs), content), files1[m] = mkfile(m5, md0, # links(m, dirs), content0), of[fd] = mkfile(m, mode, m0), dirs0 = dirs, err = ESUCCESS, m5 % VFS_PAGE_SIZE ≠ 0, ino ≠ 0, n ≠ 0, m5 < m0 + ino, afs-cons(dirs, files1), afs-cons (dirs, files1 [m, mkfile(m5, md0, # links(m, dirs), content0[m5 / VFS_PAGE_SIZE, fill(content0[m5 / VFS_PAGE_SIZE], zero, m5 % VFS_PAGE_SIZE, n1)] upto m5) ]), of-cons(of, dirs, files1), m ∈ files, fd ∈ of, m5 / VFS_PAGE_SIZE ∈ content0, m ∈ files1, n ≤ # buf0 ⊦ ⟪afs_write_inode# (mkinode (m, files1 [m, files1 [m, files1 [m, mkfile (m5, md0, # 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:= md0 ] [m ] .meta, false, files1 [m, files1 [m, files1 [m, mkfile (m5, md0, # 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:= md0 ] [m ] .nlink, 0, m0 + ino) ; err, dirs, files ; asynced); if err ≠ ESUCCESS then ino := (m0 ≤ m5 ⊃ m5 - m0;0), err := ESUCCESS; of[fd].pos := m0 + ino⟫ (dirs0 = dirs), mode ≠ MODE_W ∧ mode ≠ MODE_RW

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 103:
VFS_PAGE_SIZE = n1 + m5 % VFS_PAGE_SIZE, of[fd] = mkfile(m, mode, m0), files1[m] = mkfile(m5, md0, # links(m, dirs), content0), files[m] = mkfile(m1, md, # links(m, dirs), content), files1 [m, files1 [m, files1 [m, mkfile (m5, md0, # 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:= md0 ] [m ] = mkfile(m2, md1, m3, content1), dirs0 = dirs, err = ESUCCESS, m5 < m0 + ino, afs-cons (dirs, files1 [m, mkfile(m5, md0, # links(m, dirs), content0[m5 / VFS_PAGE_SIZE, fill(content0[m5 / VFS_PAGE_SIZE], zero, m5 % VFS_PAGE_SIZE, n1)] upto m5) ]), afs-cons(dirs, files1), of-cons(of, dirs, files1), m ∈ files1, m5 / VFS_PAGE_SIZE ∈ content0, fd ∈ of, m ∈ files, n ≤ # buf0 ⊦ ⟪afs_write_inode#(mkinode(m, md1, false, m3, 0, m0 + ino); err, dirs, files; asynced); if err ≠ ESUCCESS then ino := (m0 ≤ m5 ⊃ m5 - m0;0), err := ESUCCESS; of[fd].pos := m0 + ino⟫ (dirs0 = dirs), m5 % VFS_PAGE_SIZE = 0, ino = 0, n = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

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, md0, # 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:= md0 ] [m ], m2, md1, m3, 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: files1 [m, files1 [m, files1 [m, mkfile (m5, md0, # 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:= md0 ] [m ], m2, md1, m3, content1