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Proof step 55 from proof inv-rmdir (previous step)

(entries0[str] = m ⊃ mkdir(m0 - 1, md1, # links(entries0[str], dirs0), m2 - 1, entries0 -- str) ;mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅) ) = mkdir(m3, md2, m5, m6, entries), dirs0[m] = mkdir(m0, md1, # links(m, dirs0), m2, entries0), dirs0[entries0[str]] = mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅), dirs = dirs0[m, mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)][entries0[str], mkdir(m3, md2, m5 - 1, m6, entries)], files = files0[ino, files0[ino].size:= inode.size][ino, files0[ino, files0[ino].size:= inode.size][ino].meta:= inode.meta], ino = inode.ino, inode = mkinode(m, md, true, # links(m, dirs0), m2, m0), afs-cons(dirs0, files0), dcache-cons(dcache, dirs0, files0), icache-cons(icache, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache, pcache), ino ∈ files0, m ∈ dirs0, str ∈ entries0, entries0[str] ∈ dirs0, 1 ≤ m0, 1 ≤ m2, 1 ≤ m5, asynced1 → synced(files0, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_inode_sync#(mkinode(entries0[str], md0, true, # links(entries0[str], dirs0), m4, m1); dirs, files); p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := getinode(entries0[str], dirs, files); err := ESUCCESS; asynced := ?] ( afs-cons(dirs, files) → ⟪if err = ESUCCESS then let asynced = false in {icache_set#(c_inode, asynced; err, icache); icache_set#(p_inode, asynced; err, icache); dcache_delete#(p_inode.ino, mkdentry(str, entries0[str]).name; err, dcache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced1 → synced(files, icache, pcache)))), entries0[str] = ROOT_INO, m0 = 0, m2 = 0, m5 = 0

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ files[ino, af][ino, af0] = files[ino, af0]; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)