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Proof step 38 from proof inv-create (previous step)

dent = negdentry(str), err = ESUCCESS, afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), pw(user, dirs[ino0].meta), px(user, dirs[ino0].meta), px-parent(user, q, ROOT_INO, dirs, files), ino0 ∈ dirs ⊦ ⟪afs_lookup#(ino0, dirs, files, asynced; dent, err); if err = ESUCCESS then err := EEXISTS else if err = ENOENT then err := ESUCCESS; if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then {dent := negdentry((q + str ').last); 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) ); afs_create#(md; inode, c_inode, dent, 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 39:
dirs[ino0] = mkdir(m, md0, m0, m1, entries), dent = negdentry(str), err = ESUCCESS, afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), ino0 ∈ dirs ⊦ ⟪afs_lookup#(ino0, dirs, files, asynced; dent, err); if err = ESUCCESS then err := EEXISTS else if err = ENOENT then err := ESUCCESS; if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then {dent := negdentry((q + str ').last); inode := (ino0 ∈ dirs ⊃ mkinode(ino0, md0, true, m0, m1, m);mkinode(ino0, files[ino0].meta, false, files[ino0].nlink, 0, files[ino0].size)); afs_create#(md; inode, c_inode, dent, err, dirs, files; asynced)}⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files))

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [dirs[ino0], m, md0, m0, m1, entries]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: dirs[ino0], m, md0, m0, m1, entries