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Proof step 148 from proof refine-read (previous step)

files[m3] = mkfile(m1, md, m2, content), of[fd] = mkfile(m3, mode0, m4), ino = 0, ofh = abs-of(of), root.dir?, dom of < ino2, dom of[fd, of[fd].pos:= (m4 + ino)] < 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, of[fd].pos:= (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 ⊦ ⟨posix_read#(fd, user, root, abs-files(files); buf0, n0, err0, ofh)⟩ (ofh = abs-of(of[fd, of[fd].pos:= (m4 + ino)]) ∧ (psynced → asynced) ∧ buf1 = buf0 ∧ ino = n0 ∧ err1 = err0), mode0 ≠ MODE_R ∧ mode0 ≠ MODE_RW

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 149:
files[m3] = mkfile(m1, md, m2, content), of[fd] = mkfile(m3, mode0, m4), 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, buf0, 0, dirs, files), read-inv(m4, m4 + n0, mkinode(m3, md, false, m2, 0, m1), buf0, buf1, 0, dirs, files), fd ∈ of, n0 ≤ # buf0, m4 ≤ m1, psynced → asynced, ⌊err1⌋ ∨ err1 = ESUCCESS ⊦ ⟨posix_read#(fd, user, root, abs-files(files); buf0, n0, err0, ofh)⟩ (ofh = abs-of(of[fd, of[fd].pos:= m4]) ∧ (psynced → asynced) ∧ buf1 = buf0 ∧ 0 = n0 ∧ err1 = err0), mode0 ≠ MODE_R ∧ mode0 ≠ MODE_RW

Rule argument

Additional information

Used simplifier rules: ⊦ of[fd] = file ∧ fd ∈ of → of[fd, file] = of; (s)% ⊦ 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)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)