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Proof step 122 from proof inv-create (previous step)

dirs0[m1] = mkdir(m0, md2, # links(m1, dirs0), m4, entries1), pcache[key] = mkpentry(boolvar, buf), afs-cons(dirs0, files0), afs-cons(dirs0[m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache0, pcache), m1 ∈ dirs0, key ∈ pcache, asynced1 → synced(files0, icache0, pcache), links(m1, dirs0) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ino0 = 0, ino0 ∈ dirs0, ino0 ∈ files0, str ∈ entries1, key.data? ∧ # buf = VFS_PAGE_SIZE ∧ (key.ino = ino0 ∨ key.ino ∈ files0) ∧ ( ¬ boolvar → key.part ∈ (key.ino = ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[key.ino]).content ∧ buf = (key.ino = ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[key.ino]).content[key.part])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 123:
(key.ino = ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[key.ino]) = mkfile(m, md0, m2, content), pcache[key] = mkpentry(boolvar, buf), dirs0[m1] = mkdir(m0, md2, # links(m1, dirs0), m4, entries1), afs-cons(dirs0[m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]), afs-cons(dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache0, pcache), key ∈ pcache, m1 ∈ dirs0, asynced1 → synced(files0, icache0, pcache), links(m1, dirs0) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ino0 = 0, str ∈ entries1, ino0 ∈ files0, ino0 ∈ dirs0, key.data? ∧ # buf = VFS_PAGE_SIZE ∧ (key.ino = ino0 ∨ 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 = ino0 ⊃ mkfile(0, md, 1, ∅) ;(files0 ++ ino0)[key.ino] ), m, md0, m2, 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 = ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[key.ino]), m, md0, m2, content