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Proof step 267 from proof afs-cons-rename-file-dentry (previous step)

files[ino] = mkfile(m3, md3, m5, content), dirs0[m] = mkdir(m1, md1, # links(m, dirs0), m4, entries1), files[entries1[str0]] = mkfile(m0, md0, # links(entries1[str0], dirs0), content1), afs-cons(dirs0, files), ROOT_INO ∈ dirs0, str0 ∈ entries1, entries1[str0] ∈ files, m ∈ dirs0, ino ∈ dirs0 ∧ name ∈ dirs0[ino].entries → dirs0[ino].entries[name] ∈ dirs0 ∨ dirs0[ino].entries[name] ∈ files, ino ∈ files → ¬ ino ∈ dirs0 ∧ m5 = # links(ino, dirs0), ino ∈ dirs0 → dirs0[ino].nlink = # links(ino, dirs0) ∧ dirs0[ino].nlink ≤ 1 ∧ dirs0[ino].size = # dirs0[ino].entries ∧ dirs0[ino].nsubdirs = # subdirs(ino, dirs0), ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → dirs0[ino].entries = ∅, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries1[str0] ∈ dirs0, (ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → (ino = m ⊃ mkdir(m1, md2, # links(m, dirs0), m4, entries1);dirs0[ino]).entries = ∅) ∧ ( ino ∈ dirs0 → (ino = m ⊃ mkdir(m1, md2, # links(m, dirs0), m4, entries1);dirs0[ino]).nlink = # links(ino, dirs0) ∧ (ino = m ⊃ mkdir(m1, md2, # links(m, dirs0), m4, entries1);dirs0[ino]).nlink ≤ 1 ∧ (ino = m ⊃ mkdir(m1, md2, # links(m, dirs0), m4, entries1);dirs0[ino]).size = # (ino = m ⊃ mkdir(m1, md2, # links(m, dirs0), m4, entries1);dirs0[ino]).entries ∧ (ino = m ⊃ mkdir(m1, md2, # links(m, dirs0), m4, entries1);dirs0[ino]).nsubdirs = # subdirs(ino, dirs0)) ∧ ( ino ∈ files → ¬ ino ∈ dirs0 ∧ (ino = entries1[str0] ⊃ mkfile(m2, md, # links(entries1[str0], dirs0), content1);mkfile(m3, md3, m5, content)).nlink = # links(ino, dirs0)) ∧ ( ino ∈ dirs0 ∧ name ∈ (ino = m ⊃ mkdir(m1, md2, # links(m, dirs0), m4, entries1);dirs0[ino]).entries → (ino = m ⊃ mkdir(m1, md2, # links(m, dirs0), m4, entries1);dirs0[ino]).entries[name] ∈ dirs0 ∨ (ino = m ⊃ mkdir(m1, md2, # links(m, dirs0), m4, entries1);dirs0[ino]).entries[name] ∈ files) ∧ ( ino ∈ files ∧ n ∈ (ino = entries1[str0] ⊃ mkfile(m2, md, # links(entries1[str0], dirs0), content1);mkfile(m3, md3, m5, content)).content → # (ino = entries1[str0] ⊃ mkfile(m2, md, # links(entries1[str0], dirs0), content1);mkfile(m3, md3, m5, content)).content[n] = VFS_PAGE_SIZE)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 268:
(ino = entries1[str0] ⊃ mkfile(m2, md, # links(entries1[str0], dirs0), content1);mkfile(m3, md3, m5, content)) = mkfile(m6, md4, m7, content0), files[entries1[str0]] = mkfile(m0, md0, # links(entries1[str0], dirs0), content1), dirs0[m] = mkdir(m1, md1, # links(m, dirs0), m4, entries1), files[ino] = mkfile(m3, md3, m5, content), afs-cons(dirs0, files), m ∈ dirs0, entries1[str0] ∈ files, str0 ∈ entries1, ROOT_INO ∈ dirs0, ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → dirs0[ino].entries = ∅, ino ∈ dirs0 → dirs0[ino].nlink = # links(ino, dirs0) ∧ dirs0[ino].nlink ≤ 1 ∧ dirs0[ino].size = # dirs0[ino].entries ∧ dirs0[ino].nsubdirs = # subdirs(ino, dirs0), ino ∈ files → ¬ ino ∈ dirs0 ∧ m5 = # links(ino, dirs0), ino ∈ dirs0 ∧ name ∈ dirs0[ino].entries → dirs0[ino].entries[name] ∈ dirs0 ∨ dirs0[ino].entries[name] ∈ files, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries1[str0] ∈ dirs0, (ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → (ino = m ⊃ mkdir(m1, md2, # links(m, dirs0), m4, entries1);dirs0[ino]).entries = ∅) ∧ ( ino ∈ dirs0 → (ino = m ⊃ mkdir(m1, md2, # links(m, dirs0), m4, entries1);dirs0[ino]).nlink = # links(ino, dirs0) ∧ (ino = m ⊃ mkdir(m1, md2, # links(m, dirs0), m4, entries1);dirs0[ino]).nlink ≤ 1 ∧ (ino = m ⊃ mkdir(m1, md2, # links(m, dirs0), m4, entries1);dirs0[ino]).size = # (ino = m ⊃ mkdir(m1, md2, # links(m, dirs0), m4, entries1);dirs0[ino]).entries ∧ (ino = m ⊃ mkdir(m1, md2, # links(m, dirs0), m4, entries1);dirs0[ino]).nsubdirs = # subdirs(ino, dirs0)) ∧ (ino ∈ files → ¬ ino ∈ dirs0 ∧ m7 = # links(ino, dirs0)) ∧ ( ino ∈ dirs0 ∧ name ∈ (ino = m ⊃ mkdir(m1, md2, # links(m, dirs0), m4, entries1);dirs0[ino]).entries → (ino = m ⊃ mkdir(m1, md2, # links(m, dirs0), m4, entries1);dirs0[ino]).entries[name] ∈ dirs0 ∨ (ino = m ⊃ mkdir(m1, md2, # links(m, dirs0), m4, entries1);dirs0[ino]).entries[name] ∈ files) ∧ (ino ∈ files ∧ n ∈ content0 → # content0[n] = VFS_PAGE_SIZE)

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] → [(ino = entries1[str0] ⊃ mkfile (m2, md, # links(entries1[str0], dirs0), content1) ;mkfile(m3, md3, m5, content) ), m6, md4, m7, content0]

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: (ino = entries1[str0] ⊃ mkfile(m2, md, # links(entries1[str0], dirs0), content1) ;mkfile(m3, md3, m5, content) ), m6, md4, m7, content0