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Proof step 45 from proof refine-write (previous step)

files0 -- m2 = files -- m2, (content.stream to m).buf = splice(buf, 0, (content0.stream to m1).buf, m3, n1), files[m2] = mkfile(m1, md, # links(m2, dirs), content0), files0[m2] = mkfile(m, md, m0, content), of[fd] = mkfile(m2, mode, m3), err0 = ESUCCESS, fs = abs-files(files), ofh = abs-of(of), root.dir?, dom of < ino, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), of-cons(of, dirs, files), m2 ∈ files0, m2 ∈ files, fd ∈ of, n1 ≤ n0, n0 ≤ # buf, n1 ≤ # buf, psynced → asynced, mode = MODE_W ∨ mode = MODE_RW ⊦ fd ∈ ofh

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ fd ∈ of → of[fd] = (∅)[fd]; (s)% ⊦ fd ∈ abs-of(of) ↔ fd ∈ of; (s)