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Proof step 87 from proof refine-read (previous step)

files[m3] = mkfile(m1, md, m2, content), of[fd] = mkfile(m3, mode0, m4), ofh = abs-of(of), ino ≠ 0, root.dir?, dom of < ino2, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), of-cons(of, dirs, files), of-cons(of[fd, mkfile(m3, mode0, m4 + ino)], dirs, files), read-inv(m4, m4 + n0, mkinode(m3, md, false, m2, 0, m1), buf0, buf0, 0, dirs, files), read-inv(m4, m4 + n0, mkinode(m3, md, false, m2, 0, m1), buf0, buf1, ino, dirs, files), fd ∈ of, n0 ≤ # buf0, m4 ≤ m1, psynced → asynced, ⌊err1⌋ ∨ err1 = ESUCCESS ⊦ fd ∈ ofh ∧ (ofh[fd].mode = MODE_R ∨ ofh[fd].mode = MODE_RW) ∧ ⟨err0 := ESUCCESS; if err0 = ESUCCESS then let fh = ofh[fd] in let f = abs-files(files)[fh.fid] in choose n with n ≤ n0 ∧ fh.pos + n ≤ # f.content in {n0 := n; buf0 := copy(f.content, fh.pos, buf0, 0, n0); ofh[fd].pos := fh.pos + n0} ifnone n0 := 0 else n0 := ?⟩ (ofh = abs-of(of[fd, of[fd].pos:= (m4 + n0)]) ∧ (psynced → asynced) ∧ buf1 = buf0 ∧ ino = n0 ∧ ESUCCESS = err0), mode0 ≠ MODE_R ∧ mode0 ≠ MODE_RW

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 88:
of[fd] = mkfile(m3, mode0, m4), files[m3] = mkfile(m1, md, m2, content), ofh[fd] = mkfh(fid, mode, m), ofh = abs-of(of), root.dir?, dom of < ino2, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), of-cons(of[fd, mkfile(m3, mode0, m4 + ino)], dirs, files), of-cons(of, dirs, files), read-inv(m4, m4 + n0, mkinode(m3, md, false, m2, 0, m1), buf0, buf1, ino, dirs, files), read-inv(m4, m4 + n0, mkinode(m3, md, false, m2, 0, m1), buf0, buf0, 0, dirs, files), fd ∈ of, m4 ≤ m1, n0 ≤ # buf0, psynced → asynced, ⌊err1⌋ ∨ err1 = ESUCCESS ⊦ fd ∈ ofh ∧ (mode = MODE_R ∨ mode = MODE_RW) ∧ ⟨err0 := ESUCCESS; if err0 = ESUCCESS then let fh = ofh[fd] in let f = abs-files(files)[fh.fid] in choose n with n ≤ n0 ∧ fh.pos + n ≤ # f.content in {n0 := n; buf0 := copy(f.content, fh.pos, buf0, 0, n0); ofh[fd].pos := fh.pos + n0} ifnone n0 := 0 else n0 := ?⟩ (ofh = abs-of(of[fd, of[fd].pos:= (m4 + n0)]) ∧ (psynced → asynced) ∧ buf1 = buf0 ∧ ino = n0 ∧ ESUCCESS = err0), ino = 0, mode0 ≠ MODE_R ∧ mode0 ≠ MODE_RW

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] → [ofh[fd], fid, mode, m]

Additional information

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