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Proof step 33 from proof inv-fsync (previous step)

inode0.nlink = files1[inode0.ino].nlink, inode0.nsubdirs = 0, files0[m] = mkfile(m3, md2, # links(m, dirs), content1), files[m] = mkfile(m1, md1, # links(m, dirs), content0), afs-cons(dirs0, files1), afs-cons(dirs, files0), afs-cons(dirs, files), dcache-cons(dcache, dirs0, files1), dcache-cons(dcache, dirs, files0), dcache-cons(dcache, dirs, files), icache-cons(icache0, dirs0, files1), icache-cons(icache, dirs, files0), icache-cons(icache, dirs, files), pcache-cons(pcache0, dirs0, files1), pcache-cons(pcache0, dirs, files0), pcache-cons(pcache, dirs, files), synced(dirs0, icache0, pcache0), synced(dirs, icache, pcache0), synced(dirs, icache, pcache), inode0.ino ∈ files1, m ∈ files, m ∈ files0, ¬ inode0.directory ⊦ ⟪afs_fsync#(inode0, false, dirs0, files1; ; asynced, err)⟫ true

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 34:
files[m] = mkfile(m1, md1, # links(m, dirs), content0), files0[m] = mkfile(m3, md2, # links(m, dirs), content1), ¬ boolvar, inode0 = mkinode(m0, md, boolvar, m2, m4, m5), m2 = files1[m0].nlink, m4 = 0, afs-cons(dirs, files), afs-cons(dirs, files0), afs-cons(dirs0, files1), dcache-cons(dcache, dirs, files), dcache-cons(dcache, dirs, files0), dcache-cons(dcache, dirs0, files1), icache-cons(icache, dirs, files), icache-cons(icache, dirs, files0), icache-cons(icache0, dirs0, files1), pcache-cons(pcache, dirs, files), pcache-cons(pcache0, dirs, files0), pcache-cons(pcache0, dirs0, files1), synced(dirs, icache, pcache), synced(dirs, icache, pcache0), synced(dirs0, icache0, pcache0), m ∈ files0, m ∈ files, m0 ∈ files1 ⊦ ⟪afs_fsync#(inode0, false, dirs0, files1; ; asynced, err)⟫ true

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] → [inode0, m0, md, boolvar, m2, m4, m5]

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: inode0, m0, md, boolvar, m2, m4, m5