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Proof step 85 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), dirs0 = dirs, err0 = ESUCCESS, 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, ino1 = m0 + ino, n0 = ino, ino0 < ino1, 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, (m ∈ dirs ⊃ true ; ( VFS_PAGE_SIZE ≠ 0 ∧ m2 % VFS_PAGE_SIZE + n1 ≤ # content0[m2 / VFS_PAGE_SIZE] ∧ (m2 / VFS_PAGE_SIZE ∈ content0 ∧ VFS_PAGE_SIZE ≠ 0) ∧ VFS_PAGE_SIZE ≠ 0) ∧ ( VFS_PAGE_SIZE ≠ 0 ∧ m2 % VFS_PAGE_SIZE + n1 ≤ # content0[m2 / VFS_PAGE_SIZE] ∧ (m2 / VFS_PAGE_SIZE ∈ content0 ∧ VFS_PAGE_SIZE ≠ 0) ∧ VFS_PAGE_SIZE ≠ 0) ∧ VFS_PAGE_SIZE ≠ 0 ∧ m2 % VFS_PAGE_SIZE + n1 ≤ # content0[m2 / VFS_PAGE_SIZE] ∧ (m2 / VFS_PAGE_SIZE ∈ content0 ∧ VFS_PAGE_SIZE ≠ 0) ∧ VFS_PAGE_SIZE ≠ 0 ) ⊦ ⟪afs_check_commit#(dirs, files; err0; asynced); 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:= ino1 ; err0, dirs, files ; asynced); if err0 ≠ ESUCCESS then n0 := (m0 ≤ ino0 ⊃ ino0 - m0;0), err0 := ESUCCESS; of[fd].pos := m0 + n0⟫ (dirs0 = dirs), m2 % VFS_PAGE_SIZE = 0, ino = 0, n = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 86:
# 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

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m; (s)% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ VFS_PAGE_SIZE ≠ 0; (s)%⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkfile(m, md, m0, content).size = m; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ mkfile(m, md, m0, content).meta = md; (s)% ⊦ mkfile(m, md, m0, content).meta:= md0 = mkfile(m, md0, m0, content); (s)% ⊦ mkfile(m, md, m0, content).size:= m1 = mkfile(m1, md, m0, content); (s)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)%⊦ of-cons(of, dirs, files) ∧ fd ∈ of ∧ of[fd] = mkfile(ino, mode, n) ∧ afs-cons(dirs, files) → ¬ ino ∈ dirs; (s)