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Proof step 186 from proof inv-write (previous step)

m1 + n1 = m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE + VFS_PAGE_SIZE, VFS_PAGE_SIZE = n3 + (m0 + ino0) % VFS_PAGE_SIZE, of[fd] = mkfile(m, mode, m0), files1[m] = mkfile(m1, md, # links(m, dirs), content0), files[m] = mkfile(m2, md0, m3, content), 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 ∧ files1[ino].nlink = # links(ino, dirs), ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dirs[ino].entries = ∅, 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 ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files1, ino ∈ files1 ∧ n ∈ files1[ino].content → # files1[ino].content[n] = VFS_PAGE_SIZE ⊦ 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 ∧ (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] ) .nlink = # links(ino, dirs)) ∧ (ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files) ∧ ( ino ∈ files ∧ n ∈ (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] ) .content → # (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] ) .content [n ] = VFS_PAGE_SIZE)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 187:
m1 + n1 = m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE + VFS_PAGE_SIZE, 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 ∈ files1 ∧ n ∈ content1 → # content1[n] = VFS_PAGE_SIZE, 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 ∧ (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] ) .nlink = # links(ino, dirs)) ∧ (ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files) ∧ ( ino ∈ files ∧ n ∈ (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] ) .content → # (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] ) .content [n ] = VFS_PAGE_SIZE), 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[ino], m4, md1, m5, 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[ino], m4, md1, m5, content1