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Proof step 161 from proof inv-link (previous step)

dirs0[ino3] = mkdir(m7, md4, # links(ino3, dirs0), m12, entries2), entries1[str] = entries2[str], dirs0[ino2] = mkdir(m4, md3, # links(ino2, dirs0), m6, entries0), dirs0[m11] = mkdir(m1, md5, # links(m11, dirs0), m9, entries3), files0[entries2[str]] = mkfile(m0, md6, # links(entries2[str], dirs0), content0), entries0[str] = entries2[str], dirs0[ino0] = mkdir(m2, md1, # links(ino0, dirs0), m8, entries), entries[str] = entries2[str], dirs0[ino1] = mkdir(m5, md2, # links(ino1, dirs0), m10, entries1), pcache[key] = mkpentry(boolvar, buf), afs-cons (dirs0[m11, mkdir(m1 + 1, md0, # links(m11, dirs0), m9, entries3[str0, entries2[str]])], files0[entries2[str], mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0)]), afs-cons(dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache0, pcache), entries2[str] ∈ files0, m11 ∈ dirs0, str ∈ entries2, ino3 ∈ dirs0, str ∈ entries0, ino2 ∈ dirs0, ino0 ∈ dirs0, str ∈ entries, ino1 ∈ dirs0, str ∈ entries1, key ∈ pcache, asynced1 → synced(files0, icache0, pcache), links(ino3, dirs0) ≠ ∅ ∨ ino3 = ROOT_INO, links(m11, dirs0) ≠ ∅ ∨ m11 = ROOT_INO, links(ino2, dirs0) ≠ ∅ ∨ ino2 = ROOT_INO, links(ino0, dirs0) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ str0 ∈ entries3, key.data? ∧ # buf = VFS_PAGE_SIZE ∧ key.ino ∈ files0 ∧ ( ¬ boolvar → key.part ∈ (key.ino = entries2[str] ⊃ mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0);files0[key.ino]).content ∧ buf = (key.ino = entries2[str] ⊃ mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0);files0[key.ino]).content[key.part])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 162:
(key.ino = entries2[str] ⊃ mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0);files0[key.ino]) = mkfile(m, md7, m3, content), pcache[key] = mkpentry(boolvar, buf), dirs0[ino1] = mkdir(m5, md2, # links(ino1, dirs0), m10, entries1), entries[str] = entries2[str], dirs0[ino0] = mkdir(m2, md1, # links(ino0, dirs0), m8, entries), entries0[str] = entries2[str], files0[entries2[str]] = mkfile(m0, md6, # links(entries2[str], dirs0), content0), dirs0[m11] = mkdir(m1, md5, # links(m11, dirs0), m9, entries3), dirs0[ino2] = mkdir(m4, md3, # links(ino2, dirs0), m6, entries0), entries1[str] = entries2[str], dirs0[ino3] = mkdir(m7, md4, # links(ino3, dirs0), m12, entries2), afs-cons(dirs0, files0), afs-cons (dirs0[m11, mkdir(m1 + 1, md0, # links(m11, dirs0), m9, entries3[str0, entries2[str]])], files0[entries2[str], mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0)]), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache0, pcache), key ∈ pcache, str ∈ entries1, ino1 ∈ dirs0, str ∈ entries, ino0 ∈ dirs0, ino2 ∈ dirs0, str ∈ entries0, ino3 ∈ dirs0, str ∈ entries2, m11 ∈ dirs0, entries2[str] ∈ files0, asynced1 → synced(files0, icache0, pcache), links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino0, dirs0) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino2, dirs0) ≠ ∅ ∨ ino2 = ROOT_INO, links(m11, dirs0) ≠ ∅ ∨ m11 = ROOT_INO, links(ino3, dirs0) ≠ ∅ ∨ ino3 = ROOT_INO ⊦ str0 ∈ entries3, key.data? ∧ # buf = VFS_PAGE_SIZE ∧ key.ino ∈ files0 ∧ (¬ boolvar → key.part ∈ content ∧ buf = content[key.part])

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] → [(key.ino = entries2[str] ⊃ mkfile (m15, md, # links(entries2[str], dirs0) + 1, content0) ;files0[key.ino] ), m, md7, 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: (key.ino = entries2[str] ⊃ mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0) ;files0[key.ino] ), m, md7, m3, content