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Proof step 371 from proof inv-write (previous step)

files0[m] = mkfile(m1, md, # links(m, dirs), content0), of[fd] = mkfile(m, mode, m0), dom of < ino3, afs-cons(dirs, files0), of-cons(of, dirs, files0), of-cons(of, dirs, files0[m, mkfile(m1, md, # links(m, dirs), content0 upto m1)]), ROOT_INO ∈ dirs, fd ∈ of, m ∈ files0, n0 ≤ # buf0, ino ∈ files0 → ¬ ino ∈ dirs ∧ files0[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] ∈ files0, ino ∈ files0 ∧ n ∈ files0[ino].content → # files0[ino].content[n] = VFS_PAGE_SIZE ⊦ n0 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW, m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0, (ino ∈ files0 → ¬ ino ∈ dirs ∧ (ino = m ⊃ mkfile(m1, md, # links(m, dirs), content0 upto m1);files0[ino]).nlink = # links(ino, dirs)) ∧ ( ino ∈ files0 ∧ n ∈ (ino = m ⊃ mkfile(m1, md, # links(m, dirs), content0 upto m1);files0[ino]).content → # (ino = m ⊃ mkfile(m1, md, # links(m, dirs), content0 upto m1);files0[ino]).content[n] = VFS_PAGE_SIZE)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 372:
of[fd] = mkfile(m, mode, m0), files0[m] = mkfile(m1, md, # links(m, dirs), content0), files0[ino] = mkfile(m2, md0, m3, content), dom of < ino3, afs-cons(dirs, files0), of-cons(of, dirs, files0[m, mkfile(m1, md, # links(m, dirs), content0 upto m1)]), of-cons(of, dirs, files0), m ∈ files0, fd ∈ of, ROOT_INO ∈ dirs, n0 ≤ # buf0, ino ∈ files0 ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE, ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files0, 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 ∈ files0 → ¬ ino ∈ dirs ∧ m3 = # links(ino, dirs) ⊦ n0 = 0, (ino ∈ files0 → ¬ ino ∈ dirs ∧ (ino = m ⊃ mkfile(m1, md, # links(m, dirs), content0 upto m1);files0[ino]).nlink = # links(ino, dirs)) ∧ ( ino ∈ files0 ∧ n ∈ (ino = m ⊃ mkfile(m1, md, # links(m, dirs), content0 upto m1);files0[ino]).content → # (ino = m ⊃ mkfile(m1, md, # links(m, dirs), content0 upto m1);files0[ino]).content[n] = VFS_PAGE_SIZE), m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0, 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] → [files0[ino], m2, md0, m3, content]

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: files0[ino], m2, md0, m3, content