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Proof step 32 from proof inv-seek (previous step)

of[fd] = mkfile(m, mode, m0), err = ESUCCESS, err0 = ESUCCESS, ino = m, dom of < ino0, afs-cons(dirs, files), of-cons(of, dirs, files), fd ∈ of ⊦ of-cons(of[fd, of[fd].pos:= (getinode(ino, dirs, files).size + n)], dirs, files) ∧ dom of[fd, of[fd].pos:= (getinode(ino, dirs, files).size + n)] < ino0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 33:
⊦ of-cons(of0, dirs0, files0) → (of-cons(of1, dirs1, files1) ↔ (∀ n. (n ∈ of0 → of0[n].ino ∈ files0) → n ∈ of1 → of1[n].ino ∈ files1))
Proof step 34:
of[fd] = mkfile(m, mode, m0), dom of < ino0, afs-cons(dirs, files), of-cons(of, dirs, files), fd ∈ of, n0 ∈ of[fd, mkfile(m, mode, files[m].size + n)], n0 ∈ of, of[n0].ino ∈ files ⊦ of[fd, mkfile(m, mode, files[m].size + n)][n0].ino ∈ files

Rule argument

Additional information

Used simplifier rules: of-cons-reduce: ⊦ of-cons(of0, dirs0, files0) → ( of-cons(of1, dirs1, files1) ↔ (∀ n. (n ∈ of0 → of0[n].ino ∈ files0) → n ∈ of1 → of1[n].ino ∈ files1));%⊦ of-cons(of, dirs, files) ∧ fd ∈ of ∧ of[fd] = mkfile(ino, mode, n) → ino ∈ files; (ss)% ⊦ mkfile(m, mode, m0).ino = m; (s)% ⊦ fd = fd0 → of[fd0, file][fd] = file; (s)% ⊦ fd ∈ of[fd0, file] ↔ fd = fd0 ∨ fd ∈ of; (ws)% ⊦ mkfile(m, mode, m0).pos:= m2 = mkfile(m, mode, m2); (s)% ⊦ fd ∈ of → dom of ++ fd = dom of; (s)% ⊦ dom of[fd, file] = dom of ++ fd; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)%⊦ of-cons(of, dirs, files) ∧ fd ∈ of ∧ of[fd] = mkfile(ino, mode, n) ∧ afs-cons(dirs, files) → ¬ ino ∈ dirs; (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)