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Proof step 67 from proof fsync-others-unchanged (previous step)

icache1[ino] = mkientry(boolvar0, mkinode(m3, md2, boolvar, m4, m5, m6)), files0[ino] = mkfile(m2, md, # links(ino, dirs1), content2), files1[ino] = mkfile(m2, md, # links(ino, dirs1), content1), files1[m] = mkfile(m1, md1, # links(m, dirs1), content0), files0[m] = mkfile(m0, md0, # links(m, dirs1), content), (files ⊕ icache1)[ino] = (files1 ⊕ icache0)[ino], content1 ⊕ mkcontent(ino, pcache1) = content2 ⊕ mkcontent(ino, pcache0), afs-cons(dirs1, files1), afs-cons(dirs1, files0), dcache-cons(dcache, dirs1, files1), dcache-cons(dcache, dirs1, files0), icache-cons(icache0, dirs1, files1), icache-cons(icache0, dirs1, files0), pcache-cons(pcache1, dirs1, files1), pcache-cons(pcache0, dirs1, files0), synced(dirs1, icache0, pcache1), synced(dirs1, icache0, pcache0), ino ∈ files0, m ∈ files, m ∈ files1, m ∈ files0, ino ∈ files1, ino ∈ files, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ((files ⊕ pcache1) ⊕ icache1)[ino] = ((files0 ⊕ pcache0) ⊕ icache0)[ino], ino = m, ino ∈ icache1, ino ∈ icache1 ∧ boolvar, ino ∈ icache1 ∧ ¬ boolvar

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 68:
files[ino] = (files1 ⊕ icache0)[ino], files0[m] = mkfile(m0, md0, # links(m, dirs1), content), files1[m] = mkfile(m1, md1, # links(m, dirs1), content0), files1[ino] = mkfile(m2, md, # links(ino, dirs1), content1), files0[ino] = mkfile(m2, md, # links(ino, dirs1), content2), (∅)[ino] = mkientry(boolvar0, mkinode(m3, md2, boolvar, m4, m5, m6)), content1 ⊕ mkcontent(ino, pcache1) = content2 ⊕ mkcontent(ino, pcache0), afs-cons(dirs1, files0), afs-cons(dirs1, files1), dcache-cons(dcache, dirs1, files0), dcache-cons(dcache, dirs1, files1), icache-cons(icache0, dirs1, files0), icache-cons(icache0, dirs1, files1), pcache-cons(pcache0, dirs1, files0), pcache-cons(pcache1, dirs1, files1), synced(dirs1, icache0, pcache0), synced(dirs1, icache0, pcache1), ino ∈ files, ino ∈ files1, m ∈ files0, m ∈ files1, m ∈ files, ino ∈ files0, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ino = m, mkfile(files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache1)) = ((files0 ⊕ pcache0) ⊕ icache0)[ino], ino ∈ icache1

Rule argument

Additional information

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