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Proof step 59 from proof afs-cons-rename-dir-negdentry (previous step)

(m0 = m ⊃ mkdir(m1, md, # links(m, dirs0), m2, entries2 -- str);mkdir(m8, md5, # links(m0, dirs0), m10, entries3)) = mkdir(m4, md3, m6, m7, entries0), dirs0[m] = mkdir(m1 + 1, md, # links(m, dirs0), m2 + 1, entries2), dirs0[m0] = mkdir(m8, md5, # links(m0, dirs0), m10, entries3), dirs0[entries2[str]] = mkdir(m3, md4, # links(entries2[str], dirs0), m5, entries1), dirs = dirs0[m, mkdir(m1, md, # links(m, dirs0), m2, entries2 -- str)][m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]])], 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, md0, true, # links(m, dirs0), m2 + 1, m1 + 1), afs-cons(dirs0, files0), ino ∈ files0, str ∈ entries2, m ∈ dirs0, m0 ∈ dirs0, entries2[str] ∈ dirs0, m0 = m → md1 = md0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪afs_inode_sync#(mkinode(m0, md1, true, # links(m0, dirs0), m10, m8); dirs, files); skip; old_parent_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) ); new_parent_inode := (m0 ∈ dirs ⊃ mkinode(m0, dirs[m0].meta, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size) ;mkinode(m0, files[m0].meta, false, files[m0].nlink, 0, files[m0].size) ); err := ESUCCESS; asynced := ?⟫ afs-cons(dirs, files), str0 ∈ entries3

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)