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Proof step 181 from proof fsync-others-unchanged (previous step)

files1[m] = mkfile(m2, md, # links(m, dirs), content1), files0[m] = mkfile(m0, md0, # links(m, dirs), content), files1[ino] = mkfile(m1, md1, m3, content0), m1 = files0[ino].size, m3 = files0[ino].nlink, md1 = files0[ino].meta, content0 ⊕ mkcontent(ino, pcache1) = files0[ino].content ⊕ 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 ∈ files1, m ∈ files0, m ∈ files1, 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)), ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ((files1 ⊕ pcache1) ⊕ icache0)[ino] = ((files0 ⊕ pcache0) ⊕ icache0)[ino], ino = m

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 182:
# links(ino, dirs) = files0[ino].nlink, files1[ino] = mkfile(files0[ino].size, files0[ino].meta, files0[ino].nlink, content0), files0[m] = mkfile(m0, md0, # links(m, dirs), content), files1[m] = mkfile(m2, md, # links(m, dirs), content1), content0 ⊕ mkcontent(ino, pcache1) = files0[ino].content ⊕ 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 ∈ files0, m ∈ files1, m ∈ files0, 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)), ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ((files1 ⊕ pcache1) ⊕ icache0)[ino] = ((files0 ⊕ pcache0) ⊕ icache0)[ino], ino = m

Rule argument

Additional information

Used simplifier rules: afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base