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Proof step 130 from proof inv-create (previous step)

# files0[m3].content[m5] = VFS_PAGE_SIZE, pcache[datakey(m3, m5)] = mkpentry(false, files0[m3].content[m5]), dirs0[m1] = mkdir(m0, md2, # links(m1, dirs0), m4, entries1), (files0 ++ ino0)[m3] = mkfile(m, md0, m2, content), 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), synced(dirs0, icache0, pcache), m5 ∈ files0[m3].content, datakey(m3, m5) ∈ pcache, m1 ∈ dirs0, m3 ∈ files0, asynced1 → synced(files0, icache0, pcache), ∀ key0. key0 ∈ pcache → key0.data? ∧ # pcache[key0].page = VFS_PAGE_SIZE ∧ key0.ino ∈ files0 ∧ (¬ pcache[key0].dirty → key0.part ∈ files0[key0.ino].content ∧ pcache[key0].page = files0[key0.ino].content[key0.part]), links(m1, dirs0) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ino0 = 0, str ∈ entries1, ino0 ∈ files0, ino0 ∈ dirs0, m5 ∈ content ∧ files0[m3].content[m5] = content[m5]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 131:
# content0[m5] = VFS_PAGE_SIZE, (files0 ++ ino0)[m3] = mkfile(m, md0, m2, content), dirs0[m1] = mkdir(m0, md2, # links(m1, dirs0), m4, entries1), pcache[datakey(m3, m5)] = mkpentry(false, content0[m5]), files0[m3] = mkfile(m6, md3, m7, content0), 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, ∅)]), synced(dirs0, icache0, pcache), m3 ∈ files0, m1 ∈ dirs0, datakey(m3, m5) ∈ pcache, m5 ∈ content0, asynced1 → synced(files0, icache0, pcache), ∀ key0. key0 ∈ pcache → key0.data? ∧ # pcache[key0].page = VFS_PAGE_SIZE ∧ key0.ino ∈ files0 ∧ (¬ pcache[key0].dirty → key0.part ∈ files0[key0.ino].content ∧ pcache[key0].page = files0[key0.ino].content[key0.part]), links(m1, dirs0) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ino0 = 0, ino0 ∈ dirs0, ino0 ∈ files0, str ∈ entries1, m5 ∈ content ∧ content0[m5] = content[m5]

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[m3], m6, md3, 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: files0[m3], m6, md3, m7, content0