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Proof step 189 from proof inv-write (previous step)

m1 + n1 = m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE + VFS_PAGE_SIZE, (ino = m ⊃ mkfile(m2, md0, m3, content[(m0 + ino0) / VFS_PAGE_SIZE, copy(buf0, ino0, zeropage, (m0 + ino0) % VFS_PAGE_SIZE, min(n4, n3))]) ;files[ino] ) = mkfile(m6, md2, m7, content2), VFS_PAGE_SIZE = n3 + (m0 + ino0) % VFS_PAGE_SIZE, files[m] = mkfile(m2, md0, m3, content), files1[m] = mkfile(m1, md, # links(m, dirs), content0), of[fd] = mkfile(m, mode, m0), files1[ino] = mkfile(m4, md1, m5, content1), m1 = n2 + m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, dom of < ino3, afs-cons(dirs, files), afs-cons(dirs, files1), of-cons (of, dirs, files[m, mkfile(m2, md0, m3, content[(m0 + ino0) / VFS_PAGE_SIZE, copy(buf0, ino0, zeropage, (m0 + ino0) % VFS_PAGE_SIZE, min(n4, n3))])]), of-cons(of, dirs, files1), of-cons(of, dirs, files), fd ∈ of, m1 / VFS_PAGE_SIZE ∈ content0, m ∈ files1, ROOT_INO ∈ dirs, ino0 + min(n4, n3) ≤ # buf0, (m0 + ino0) % VFS_PAGE_SIZE + min(n4, n3) ≤ VFS_PAGE_SIZE, n2 + n1 ≤ VFS_PAGE_SIZE, n4 + ino0 ≤ # buf0, ino0 ≤ # buf0, ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files1, ino ∈ dirs → dirs[ino].nlink = # links(ino, dirs) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs), ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dirs[ino].entries = ∅, ino ∈ files1 → ¬ ino ∈ dirs ∧ m5 = # links(ino, dirs) ⊦ n4 + ino0 = 0, min(n4, n3) = 0, n2 = 0, (m0 + ino0) / VFS_PAGE_SIZE ∈ content, (ino ∈ files → ¬ ino ∈ dirs ∧ m7 = # links(ino, dirs)) ∧ (ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files) ∧ (ino ∈ files ∧ n ∈ content2 → # content2[n] = VFS_PAGE_SIZE), mode ≠ MODE_W ∧ mode ≠ MODE_RW

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 190:
m1 + n1 = m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE + VFS_PAGE_SIZE, (ino = m ⊃ mkfile(m2, md0, m3, content[(m0 + ino0) / VFS_PAGE_SIZE, copy(buf0, ino0, zeropage, (m0 + ino0) % VFS_PAGE_SIZE, min(n4, n3))]) ;files[ino] ) = mkfile(m6, md2, m7, content2), VFS_PAGE_SIZE = n3 + (m0 + ino0) % VFS_PAGE_SIZE, files1[ino] = mkfile(m4, md1, m5, content1), of[fd] = mkfile(m, mode, m0), files1[m] = mkfile(m1, md, # links(m, dirs), content0), files[m] = mkfile(m2, md0, m3, content), dirs[ino] = mkdir(m8, md3, m9, m10, entries), m1 = n2 + m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, dom of < ino3, afs-cons(dirs, files1), afs-cons(dirs, files), of-cons(of, dirs, files), of-cons(of, dirs, files1), of-cons (of, dirs, files[m, mkfile(m2, md0, m3, content[(m0 + ino0) / VFS_PAGE_SIZE, copy(buf0, ino0, zeropage, (m0 + ino0) % VFS_PAGE_SIZE, min(n4, n3))])]), ROOT_INO ∈ dirs, m ∈ files1, m1 / VFS_PAGE_SIZE ∈ content0, fd ∈ of, ino0 ≤ # buf0, n4 + ino0 ≤ # buf0, n2 + n1 ≤ VFS_PAGE_SIZE, (m0 + ino0) % VFS_PAGE_SIZE + min(n4, n3) ≤ VFS_PAGE_SIZE, ino0 + min(n4, n3) ≤ # buf0, ino ∈ files1 → ¬ ino ∈ dirs ∧ m5 = # links(ino, dirs), ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → entries = ∅, ino ∈ dirs → m9 = # links(ino, dirs) ∧ m9 ≤ 1 ∧ m8 = # entries ∧ m10 = # subdirs(ino, dirs), ino ∈ dirs ∧ name ∈ entries → entries[name] ∈ dirs ∨ entries[name] ∈ files1 ⊦ n4 + ino0 = 0, min(n4, n3) = 0, n2 = 0, (m0 + ino0) / VFS_PAGE_SIZE ∈ content, mode ≠ MODE_W ∧ mode ≠ MODE_RW, (ino ∈ files → ¬ ino ∈ dirs ∧ m7 = # links(ino, dirs)) ∧ (ino ∈ dirs ∧ name ∈ entries → entries[name] ∈ dirs ∨ entries[name] ∈ files) ∧ (ino ∈ files ∧ n ∈ content2 → # content2[n] = VFS_PAGE_SIZE)

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [dirs[ino], m8, md3, m9, m10, entries]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: dirs[ino], m8, md3, m9, m10, entries