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Proof step 41 from proof fsync-inode-inv (previous step)

files[m] = mkfile(m0, md0, # links(m, dirs), content), icache[m] = mkientry(true, inode1), err = ESUCCESS, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ files, m ∈ icache, inode1.ino ∈ dirs ∧ inode1.nlink = dirs[inode1.ino].nlink ∧ inode1.size = dirs[inode1.ino].size ∧ inode1.nsubdirs = dirs[inode1.ino].nsubdirs ∧ inode1.directory ∨ inode1.ino ∈ files ∧ inode1.nlink = files[inode1.ino].nlink ∧ inode1.nsubdirs = 0 ∧ ¬ inode1.directory ⊦ [afs_write_inode#(inode1; err, dirs, files; asynced1)] ( afs-cons(dirs, files) → ⟪inode := inode1; if err = ESUCCESS then {asynced := false; icache_set_status#(m, asynced; err, icache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ inode.ino ∈ files ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 42:
icache[m] = mkientry(true, inode1), files[m] = mkfile(m0, md0, # links(m, dirs), content), err = ESUCCESS, inode1 = mkinode(m1, md, boolvar, m2, m3, m4), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ icache, m ∈ files, m1 ∈ dirs ∧ m2 = dirs[m1].nlink ∧ m4 = dirs[m1].size ∧ m3 = dirs[m1].nsubdirs ∧ boolvar ∨ m1 ∈ files ∧ m2 = files[m1].nlink ∧ m3 = 0 ∧ ¬ boolvar ⊦ [afs_write_inode#(inode1; err, dirs, files; asynced1)] ( afs-cons(dirs, files) → ⟪inode := inode1; if err = ESUCCESS then {asynced := false; icache_set_status#(m, asynced; err, icache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ inode.ino ∈ files ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory))

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] → [inode1, m1, md, boolvar, m2, m3, m4]

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: inode1, m1, md, boolvar, m2, m3, m4