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Proof step 86 from proof write-term (previous step)

# links(m, dirs) = files[m].nlink, VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, of[fd] = mkfile(m, mode, m0), files1[m] = mkfile(m2, md0, files[m].nlink, content0), err0 = ESUCCESS, m2 % VFS_PAGE_SIZE ≠ 0, ino ≠ 0, n ≠ 0, m2 < m0 + ino, afs-cons (dirs, files1[m, mkfile(m2, md0, files[m].nlink, content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)] upto m2)]), afs-cons(dirs, files1), of-cons(of, dirs, files1), m ∈ files1, m2 / VFS_PAGE_SIZE ∈ content0, fd ∈ of, m ∈ files, n ≤ # buf0 ⊦ ⟪afs_check_commit#(dirs, files; err0; asynced); ino0 := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, files1 [m, files1 [m, files1 [m, mkfile (m2, md0, files[m].nlink, content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ] [m ] .size:= m2 ] [m ] .meta:= md0 ] [m ] .meta, false, files1 [m, files1 [m, files1 [m, mkfile (m2, md0, files[m].nlink, content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ] [m ] .size:= m2 ] [m ] .meta:= md0 ] [m ] .nlink, 0, files1 [m, files1 [m, files1 [m, mkfile (m2, md0, files[m].nlink, content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ] [m ] .size:= m2 ] [m ] .meta:= md0 ] [m ] .size) ) .size; dirs0 := dirs; if err0 = ESUCCESS then afs_write_inode# ( (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, files1 [m, files1 [m, files1 [m, mkfile (m2, md0, files[m].nlink, content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ] [m ] .size:= m2 ] [m ] .meta:= md0 ] [m ] .meta, false, files1 [m, files1 [m, files1 [m, mkfile (m2, md0, files[m].nlink, content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ] [m ] .size:= m2 ] [m ] .meta:= md0 ] [m ] .nlink, 0, files1 [m, files1 [m, files1 [m, mkfile (m2, md0, files[m].nlink, content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ] [m ] .size:= m2 ] [m ] .meta:= md0 ] [m ] .size) ) .size:= (m0 + ino) ; err0, dirs, files ; asynced); if err0 ≠ ESUCCESS then ino := (m0 ≤ ino0 ⊃ ino0 - m0;0), err0 := 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 87:
# links(m, dirs) = files[m].nlink, (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, files1 [m, files1 [m, files1 [m, mkfile (m2, md0, files[m].nlink, content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ] [m ] .size:= m2 ] [m ] .meta:= md0 ] [m ] .meta, false, files1 [m, files1 [m, files1 [m, mkfile (m2, md0, files[m].nlink, content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ] [m ] .size:= m2 ] [m ] .meta:= md0 ] [m ] .nlink, 0, files1 [m, files1 [m, files1 [m, mkfile (m2, md0, files[m].nlink, content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ] [m ] .size:= m2 ] [m ] .meta:= md0 ] [m ] .size) ) = mkinode(m1, md, boolvar, m3, m4, m5), VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, files1[m] = mkfile(m2, md0, files[m].nlink, content0), of[fd] = mkfile(m, mode, m0), err0 = ESUCCESS, m2 < m0 + ino, afs-cons(dirs, files1), afs-cons (dirs, files1[m, mkfile(m2, md0, files[m].nlink, content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)] upto m2)]), of-cons(of, dirs, files1), m ∈ files, fd ∈ of, m2 / VFS_PAGE_SIZE ∈ content0, m ∈ files1, n ≤ # buf0 ⊦ ⟪afs_check_commit#(dirs, files; err0; asynced); ino0 := m5; dirs0 := dirs; if err0 = ESUCCESS then afs_write_inode# ( (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, files1 [m, files1 [m, files1 [m, mkfile (m2, md0, files[m].nlink, content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ] [m ] .size:= m2 ] [m ] .meta:= md0 ] [m ] .meta, false, files1 [m, files1 [m, files1 [m, mkfile (m2, md0, files[m].nlink, content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ] [m ] .size:= m2 ] [m ] .meta:= md0 ] [m ] .nlink, 0, files1 [m, files1 [m, files1 [m, mkfile (m2, md0, files[m].nlink, content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ] [m ] .size:= m2 ] [m ] .meta:= md0 ] [m ] .size) ) .size:= (m0 + ino) ; err0, dirs, files ; asynced); if err0 ≠ ESUCCESS then ino := (m0 ≤ ino0 ⊃ ino0 - m0;0), err0 := ESUCCESS; of[fd].pos := m0 + ino⟫ (dirs0 = dirs), m2 % VFS_PAGE_SIZE = 0, ino = 0, n = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [(m ∈ dirs ⊃ mkinode (m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, files1 [m, files1 [m, files1 [m, mkfile (m2, md0, files[m].nlink, content0 [m2 / VFS_PAGE_SIZE, fill (content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1) ] upto m2) ] [m ] .size:= m2 ] [m ] .meta:= md0 ] [m ] .meta, false, files1 [m, files1 [m, files1 [m, mkfile (m2, md0, files[m].nlink, content0 [m2 / VFS_PAGE_SIZE, fill (content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1) ] upto m2) ] [m ] .size:= m2 ] [m ] .meta:= md0 ] [m ] .nlink, 0, files1 [m, files1 [m, files1 [m, mkfile (m2, md0, files[m].nlink, content0 [m2 / VFS_PAGE_SIZE, fill (content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1) ] upto m2) ] [m ] .size:= m2 ] [m ] .meta:= md0 ] [m ] .size) ), m1, md, boolvar, m3, m4, m5]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: (m ∈ dirs ⊃ mkinode (m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, files1 [m, files1 [m, files1 [m, mkfile (m2, md0, files[m].nlink, content0 [m2 / VFS_PAGE_SIZE, fill (content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1) ] upto m2) ] [m ] .size:= m2 ] [m ] .meta:= md0 ] [m ] .meta, false, files1 [m, files1 [m, files1 [m, mkfile (m2, md0, files[m].nlink, content0 [m2 / VFS_PAGE_SIZE, fill (content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1) ] upto m2) ] [m ] .size:= m2 ] [m ] .meta:= md0 ] [m ] .nlink, 0, files1 [m, files1 [m, files1 [m, mkfile (m2, md0, files[m].nlink, content0 [m2 / VFS_PAGE_SIZE, fill (content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1) ] upto m2) ] [m ] .size:= m2 ] [m ] .meta:= md0 ] [m ] .size) ), m1, md, boolvar, m3, m4, m5