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Proof step 32 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), 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, fd ∈ of, m2 ∈ files, n1 ≤ n0, n0 ≤ # buf, n1 ≤ # buf, psynced → asynced, mode = MODE_W ∨ mode = MODE_RW ⊦ ∃ n. n ≤ n0 ∧ ⟨n0 := n; f := mkfile(abs-files(files)[abs-of(of)[fd].fid].meta, splice(buf, 0, abs-files(files)[abs-of(of)[fd].fid].content, abs-of(of)[fd].pos, n0)); fs := abs-files(files)[abs-of(of)[fd].fid, f]; ofh := abs-of(of)[fd, mkfh(abs-of(of)[fd].fid, abs-of(of)[fd].mode, abs-of(of)[fd].pos + n0)]; psynced := ?⟩ (ofh = abs-of(of[fd, of[fd].pos:= (m3 + n0)]) ∧ fs = abs-files(files0) ∧ (psynced → asynced0) ∧ n1 = n0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 33:
files0 -- m2 = files -- m2, (content.stream to m).buf = splice(buf, 0, (content0.stream to m1).buf, m3, n1), of[fd] = mkfile(m2, mode, m3), files0[m2] = mkfile(m, md, m0, content), files[m2] = mkfile(m1, md, # links(m2, dirs), content0), abs-of(of)[fd] = mkfh(fid, mode0, m4), 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 ∈ files, fd ∈ of, m2 ∈ files0, n1 ≤ # buf, n0 ≤ # buf, n1 ≤ n0, psynced → asynced, mode = MODE_W ∨ mode = MODE_RW ⊦ ∃ n. n ≤ n0 ∧ ⟨n0 := n; f := mkfile(abs-files(files)[fid].meta, splice(buf, 0, abs-files(files)[fid].content, m4, n0)); fs := abs-files(files)[fid, f]; ofh := abs-of(of)[fd, mkfh(fid, mode0, m4 + n0)]; psynced := ?⟩ (ofh = abs-of(of[fd, of[fd].pos:= (m3 + n0)]) ∧ fs = abs-files(files0) ∧ (psynced → asynced0) ∧ n1 = n0)

Rule argument

spec: file-handle name: elim seq: ⊦ (fid = fh.fid ∧ mode = fh.mode) ∧ m = fh.pos ↔ fh = mkfh(fid, mode, m) subst: [fh, fid, mode, m] → [abs-of(of)[fd], fid, mode0, m4]

Additional information

Used simplifier rules: ⊦ (fid = fh.fid ∧ mode = fh.mode) ∧ m = fh.pos ↔ fh = mkfh(fid, mode, m); (elim) Used terms: abs-of(of)[fd], fid, mode0, m4