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Proof step 160 from proof refine-read (previous step)

of[fd] = mkfile(m3, mode0, m4), files[m3] = mkfile(m1, md, m2, content), err0 = err1, err0 = ESUCCESS, f = abs-files(files)[fh.fid], fh = ofh[fd], 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, dirs, files), read-inv(m4, m4 + n0, mkinode(m3, md, false, m2, 0, m1), buf0, buf1, 0, dirs, files), read-inv(m4, m4 + n0, mkinode(m3, md, false, m2, 0, m1), buf0, buf0, 0, dirs, files), fd ∈ ofh, fd ∈ of, fh.fid ∈ abs-files(files), m4 ≤ m1, n0 ≤ # buf0, psynced → asynced, ⌊err1⌋ ∨ err1 = ESUCCESS ⊦ (∀ n. ¬(n ≤ n0 ∧ fh.pos + n ≤ # f.content)) ∧ ⟨n0 := 0⟩ (ofh = abs-of(of[fd, of[fd].pos:= m4]) ∧ (psynced → asynced) ∧ buf1 = buf0 ∧ 0 = n0 ∧ err1 = err0), ∃ n. (n ≤ n0 ∧ fh.pos + n ≤ # f.content) ∧ ⟨n0 := n; buf0 := copy(f.content, fh.pos, buf0, 0, n0); ofh[fd].pos := fh.pos + n0⟩ (ofh = abs-of(of[fd, of[fd].pos:= m4]) ∧ (psynced → asynced) ∧ buf1 = buf0 ∧ 0 = n0 ∧ err1 = err0), mode0 ≠ MODE_R ∧ mode0 ≠ MODE_RW

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 161:
files[m3] = mkfile(m1, md, # links(m3, dirs), content), of[fd] = mkfile(m3, mode0, m4), 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), read-inv(m4, m4 + n0, mkinode(m3, md, false, # links(m3, dirs), 0, m1), buf0, buf0, 0, dirs, files), read-inv(m4, m4 + n0, mkinode(m3, md, false, # links(m3, dirs), 0, m1), buf0, buf1, 0, dirs, files), m3 ∈ files, fd ∈ of, n0 ≤ # buf0, m4 ≤ m1, psynced → asynced ⊦ (¬ n ≤ n0 ∨ ¬ of[fd].pos + n ≤ files[of[fd].ino].size) ∧ ⟨n0 := 0⟩ (abs-of(of) = abs-of(of[fd, of[fd].pos:= m4]) ∧ (psynced → asynced) ∧ buf1 = buf0 ∧ 0 = n0), ∃ n1. n1 ≤ n0 ∧ of[fd].pos + n1 ≤ files[of[fd].ino].size ∧ ⟨n0 := n1; buf0 := copy(abs-files(files)[abs-of(of)[fd].fid].content, abs-of(of)[fd].pos, buf0, 0, n0); ofh := abs-of(of)[fd, mkfh(abs-of(of)[fd].fid, abs-of(of)[fd].mode, abs-of(of)[fd].pos + n0)]⟩ (ofh = abs-of(of[fd, of[fd].pos:= m4]) ∧ (psynced → asynced) ∧ buf1 = buf0 ∧ 0 = n0), mode0 ≠ MODE_R ∧ mode0 ≠ MODE_RW

Rule argument

Additional information

Used simplifier rules: afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base% ⊦ fh.pos:= m = mkfh(fh.fid, fh.mode, m); (s)% ⊦ ⌜m⌝ .n = m; (s)%¬ # σ0 < ⌜n⌝ ⊦ #(σ0 to n) = ⌜n⌝ ; (s)% ⊦ ¬ ∞ < n∞; (s)% ⊦ # content.stream = ∞; (s)%finp(σ) ⊦ # σ.buf = (# σ).n; (s)% ⊦ finp(σ0 to m); (s)% ⊦ mkfile(m, mode, m0).ino = m; (s)% ⊦ mkfile(md, buf).content = buf; (s)%⊦ ino ∈ files → abs-files(files)[⌜ino⌝ ] = mkfile (files[ino].meta, (files[ino].content.stream to files[ino].size).buf); (s)% ⊦ mkfh(fid, mode, m).pos = m; (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)% ⊦ fd ∈ abs-of(of) ↔ fd ∈ of; (s)% ⊦ ⌜ino⌝ ∈ abs-files(files) ↔ ino ∈ files; (s)% ⊦ mkfh(fid, mode, m).fid = fid; (s)%fd ∈ of ⊦ abs-of(of)[fd] = mkfh(⌜of[fd].ino⌝ , of[fd].mode, of[fd].pos); (s)