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Proof step 247 from proof inv-rename-dir-negdentry (previous step)

(m = m9 ⊃ mkdir(m1, md, # links(m9, dirs0), m2, entries0 -- str);mkdir(m8, md5, # links(m, dirs0), m10, entries3)) = mkdir(m4, md3, m6, m7, entries2), (m9 = m ⊃ mkdir(m4 + 1, md4, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md0, # links(m9, dirs0), m2, entries0 -- str)) = mkdir(m0, md1, m11, m12, entries1), (m = m9 ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])) = mkdir(m13, md6, m14, m15, entries4), dirs0[entries0[str]] = mkdir(m3, md2, # links(entries0[str], dirs0), m5, entries), dirs0[m] = mkdir(m8, md5, # links(m, dirs0), m10, entries3), dirs0[m9] = mkdir(m1 + 1, md, # links(m9, dirs0), m2 + 1, entries0), afs-cons(dirs0, files), afs-cons (dirs0 [m9, (m9 = m ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m9, dirs0), m2, entries0 -- str)).meta:= md0 ] [m, mkdir(m13, md4, m14, m15, entries4) ], files), icache-cons(icache0, dirs0, files), synced(dirs0, icache0, pcache), entries0[str] ∈ dirs0, m ∈ dirs0, str ∈ entries0, m9 ∈ dirs0, m = m9 → md4 = md0, asynced2 → synced(files, icache0, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m9, dirs0) ≠ ∅ ∨ m9 = ROOT_INO ⊦ str0 ∈ entries3, ∀ ino. ino ∈ icache0[m9, mkientry(false, mkinode(m9, md1, true, m11, m12, m0))][m, mkientry(false, mkinode(m, md4, true, m14, m15, m13))] → icache0[m9, mkientry(false, mkinode(m9, md1, true, m11, m12, m0))][m, mkientry(false, mkinode(m, md4, true, m14, m15, m13))][ino].inode.ino = ino ∧ (icache0[m9, mkientry(false, mkinode(m9, md1, true, m11, m12, m0))][m, mkientry(false, mkinode(m, md4, true, m14, m15, m13))][ino].dirty ⊃ valid-file-inode (icache0[m9, mkientry(false, mkinode(m9, md1, true, m11, m12, m0))][m, mkientry(false, mkinode(m, md4, true, m14, m15, m13))][ino].inode, dirs0 [m9, (m9 = m ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m9, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m, mkdir(m13, md4, m14, m15, entries4) ], files) ; valid-ino (ino, dirs0 [m9, (m9 = m ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m9, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m, mkdir(m13, md4, m14, m15, entries4) ], files) ∧ valid-inode (icache0[m9, mkientry(false, mkinode(m9, md1, true, m11, m12, m0))][m, mkientry(false, mkinode(m, md4, true, m14, m15, m13))][ino].inode, dirs0 [m9, (m9 = m ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m9, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m, mkdir(m13, md4, m14, m15, entries4) ], files) )

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries).meta:= md0 = mkdir(m, md0, m0, m1, entries); (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)%⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)%⊦ valid-inode(inode, dirs, files) ↔ inode = getinode(inode.ino, dirs, files); (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)