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Proof step 75 from proof write-term (previous step)

VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, of[fd] = mkfile(m, mode, m0), files1[m] = mkfile(m2, md0, # links(m, dirs), content0), err = ESUCCESS, files0 = files1 [m, mkfile(m2, md0, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ], ino3 = 0, afs-cons (dirs, files1 [m, mkfile(m2, md0, # links(m, dirs), 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, n0 ≤ # buf0 ⊦ ∀ ino3, err, files0, asynced. m ∈ files0 ∧ # links(m, dirs) = files0[m].nlink → ⟪if ino3 ≠ 0 then err := ESUCCESS; dirs0 := dirs; if err = ESUCCESS then let 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, # links(m, dirs), 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, # links(m, dirs), 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, # links(m, dirs), 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 in {n0 := ino3, ino1 := m0 + ino3; if ino3 ≠ 0 ∧ ino0 < ino1 then {inode0 := (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, # links(m, dirs), 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, # links(m, dirs), 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, # links(m, dirs), 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:= ino1; afs_check_commit#(dirs, files0; err; asynced); if err = ESUCCESS then afs_write_inode#(inode0; err, dirs, files0; asynced)}; if err ≠ ESUCCESS then n0 := (m0 ≤ ino0 ⊃ ino0 - m0;0), err := ESUCCESS; of[fd].pos := m0 + n0}⟫ (dirs0 = dirs), m2 % VFS_PAGE_SIZE = 0, n0 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 76:
# links(m, dirs) = files[m].nlink, VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, files1[m] = mkfile(m2, md0, files[m].nlink, content0), of[fd] = mkfile(m, mode, m0), m2 % VFS_PAGE_SIZE ≠ 0, n0 ≠ 0, 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, n0 ≤ # buf0 ⊦ ⟪if ino ≠ 0 then err0 := ESUCCESS; dirs0 := dirs; if err0 = ESUCCESS then let 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 in {n0 := ino, ino1 := m0 + ino; if ino ≠ 0 ∧ ino0 < ino1 then {inode0 := (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:= ino1; afs_check_commit#(dirs, files; err0; asynced); if err0 = ESUCCESS then afs_write_inode#(inode0; err0, dirs, files; asynced)}; if err0 ≠ ESUCCESS then n0 := (m0 ≤ ino0 ⊃ ino0 - m0;0), err0 := ESUCCESS; of[fd].pos := m0 + n0}⟫ (dirs0 = dirs), mode ≠ MODE_W ∧ mode ≠ MODE_RW

Rule argument

Additional information

Used simplifier rules: afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base