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Proof step 206 from proof fsync-others-unchanged (previous step)

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), 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. 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 ∧ icache0[ino].inode.directory

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 207:
icache0[ino].inode = 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

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [icache0[ino].inode, m3, md2, boolvar, m4, m5, m6]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: icache0[ino].inode, m3, md2, boolvar, m4, m5, m6