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Proof step 209 from proof fsync-others-unchanged (previous step)

icache0[ino] = mkientry(boolvar0, mkinode(m3, md2, boolvar, m4, m5, m6)), files0[ino] = mkfile(m2, md1, # links(ino, dirs), content2), files1[ino] = mkfile(m2, md1, # links(ino, dirs), content1), files1[m] = mkfile(m1, md, # links(m, dirs), content0), files0[m] = mkfile(m0, md0, # links(m, dirs), content), content1 ⊕ mkcontent(ino, pcache1) = content2 ⊕ mkcontent(ino, pcache0), afs-cons(dirs, files0), afs-cons(dirs, files1), dcache-cons(dcache, dirs, files0), dcache-cons(dcache, dirs, files1), icache-cons(icache0, dirs, files0), icache-cons(icache0, dirs, files1), pcache-cons(pcache0, dirs, files0), pcache-cons(pcache1, dirs, files1), synced(dirs, icache0, pcache0), synced(dirs, icache0, pcache1), ino ∈ files0, m ∈ files0, m ∈ files1, ino ∈ files1, ∀ ino. ino ≠ m ∧ ino ∈ files0 → ino ∈ files1 ∧ mkfile(files1[ino].size, files1[ino].meta, files1[ino].nlink, files1[ino].content ⊕ mkcontent(ino, pcache1)) = mkfile(files0[ino].size, files0[ino].meta, files0[ino].nlink, files0[ino].content ⊕ mkcontent(ino, pcache0)) ⊦ ((files1 ⊕ pcache1) ⊕ icache0)[ino] = ((files0 ⊕ pcache0) ⊕ icache0)[ino], err0 = ESUCCESS, ino = m, ino ∈ icache0 ∧ boolvar

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 210:
files0[m] = mkfile(m0, md0, # links(m, dirs), content), files1[m] = mkfile(m1, md, # links(m, dirs), content0), files1[ino] = mkfile(m2, md1, # links(ino, dirs), content1), files0[ino] = mkfile(m2, md1, # links(ino, dirs), content2), icache0[ino] = mkientry(boolvar0, mkinode(m3, md2, boolvar, m4, m5, m6)), content1 ⊕ mkcontent(ino, pcache1) = content2 ⊕ mkcontent(ino, pcache0), afs-cons(dirs, files1), afs-cons(dirs, files0), dcache-cons(dcache, dirs, files1), dcache-cons(dcache, dirs, files0), icache-cons(icache0, dirs, files1), icache-cons(icache0, dirs, files0), pcache-cons(pcache1, dirs, files1), pcache-cons(pcache0, dirs, files0), synced(dirs, icache0, pcache1), synced(dirs, icache0, pcache0), ino ∈ files1, m ∈ files1, m ∈ files0, ino ∈ files0, ino ∈ icache0, ∀ ino. ino ≠ m ∧ ino ∈ files0 → ino ∈ files1 ∧ mkfile(files1[ino].size, files1[ino].meta, files1[ino].nlink, files1[ino].content ⊕ mkcontent(ino, pcache1)) = mkfile(files0[ino].size, files0[ino].meta, files0[ino].nlink, files0[ino].content ⊕ mkcontent(ino, pcache0)) ⊦ ((files1 ⊕ pcache1) ⊕ icache0)[ino] = ((files0 ⊕ pcache0) ⊕ icache0)[ino], err0 = ESUCCESS, ino = m, ino ∈ icache0 ∧ boolvar

Rule argument

fma: ino ∈ icache0

Additional information

Used simplifier rules: ⊦ ¬ ino ∈ icache → icache[ino] = (∅)[ino]; (s)% ⊦ ¬ ino ∈ icache → (files ⊕ icache)[ino] = files[ino]; (s)%⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache)); (s)% ⊦ mkfile(m, md, m0, content).size = m; (s)% ⊦ mkfile(m, md, m0, content).meta = md; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ mkfile(m, md, m0, content).content = content; (s) Used formulas: ino ∈ icache0