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Proof step 23 from proof inv-writemeta (previous step)

err = ESUCCESS, afs-cons(dirs, files), ispath(p, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), pw (user, (ino0 ∈ dirs ⊃ mkinode(ino0, dirs[ino0].meta, true, dirs[ino0].nlink, dirs[ino0].nsubdirs, dirs[ino0].size) ;mkinode(ino0, files[ino0].meta, false, files[ino0].nlink, 0, files[ino0].size) ) .meta), px-parent(user, p, ROOT_INO, dirs, files), ino0 ∈ dirs ∨ ino0 ∈ files ⊦ ⟪afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then afs_write_inode# ( (ino0 ∈ dirs ⊃ mkinode(ino0, dirs[ino0].meta, true, dirs[ino0].nlink, dirs[ino0].nsubdirs, dirs[ino0].size) ;mkinode(ino0, files[ino0].meta, false, files[ino0].nlink, 0, files[ino0].size) ) .meta:= md ; err, dirs, files ; asynced)⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 24:
(ino0 ∈ dirs ⊃ mkinode(ino0, dirs[ino0].meta, true, dirs[ino0].nlink, dirs[ino0].nsubdirs, dirs[ino0].size) ;mkinode(ino0, files[ino0].meta, false, files[ino0].nlink, 0, files[ino0].size) ) = mkinode(m, md0, boolvar, m0, m1, m2), err = ESUCCESS, afs-cons(dirs, files), ispath(p, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), pw(user, md0), px-parent(user, p, ROOT_INO, dirs, files), ino0 ∈ dirs ∨ ino0 ∈ files ⊦ ⟪afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then afs_write_inode# ( (ino0 ∈ dirs ⊃ mkinode(ino0, dirs[ino0].meta, true, dirs[ino0].nlink, dirs[ino0].nsubdirs, dirs[ino0].size) ;mkinode(ino0, files[ino0].meta, false, files[ino0].nlink, 0, files[ino0].size) ) .meta:= md ; err, dirs, files ; asynced)⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files))

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] → [(ino0 ∈ dirs ⊃ mkinode (ino0, dirs[ino0].meta, true, dirs[ino0].nlink, dirs[ino0].nsubdirs, dirs[ino0].size) ;mkinode (ino0, files[ino0].meta, false, files[ino0].nlink, 0, files[ino0].size) ), m, md0, boolvar, m0, m1, m2]

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: (ino0 ∈ dirs ⊃ mkinode (ino0, dirs[ino0].meta, true, dirs[ino0].nlink, dirs[ino0].nsubdirs, dirs[ino0].size) ;mkinode (ino0, files[ino0].meta, false, files[ino0].nlink, 0, files[ino0].size) ), m, md0, boolvar, m0, m1, m2