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Proof step 118 from proof refine-read (previous step)

of[fd] = mkfile(m, mode, m0), files[m] = mkfile(m1, md, # links(m, dirs), content), 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(m, mode, m0 + ino)], dirs, files), read-inv(m0, m0 + n0, mkinode(m, md, false, # links(m, dirs), 0, m1), buf0, buf0, 0, dirs, files), read-inv(m0, m0 + n0, mkinode(m, md, false, # links(m, dirs), 0, m1), buf0, buf1, ino, dirs, files), m ∈ files, fd ∈ of, n ≤ n0, n ≤ # buf0, n0 ≤ # buf0, m0 ≤ m1, m0 + n ≤ m1, psynced → asynced, ⌊err1⌋ ∨ err1 = ESUCCESS ⊦ ino = 0, mode ≠ MODE_R ∧ mode ≠ MODE_RW, (m0 + ino ≤ # (content.stream to m1).buf ∧ 0 + ino ≤ # buf0) ∧ (finp(content.stream) → ⌜m1⌝ < # content.stream ∨ ⌜m1⌝ = # content.stream)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 119:
files[m] = mkfile(m1, md, # links(m, dirs), content), of[fd] = mkfile(m, mode, m0), 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(m, mode, m0 + ino)], dirs, files), of-cons(of, dirs, files), read-inv(m0, m0 + n0, mkinode(m, md, false, # links(m, dirs), 0, m1), buf0, buf1, ino, dirs, files), read-inv(m0, m0 + n0, mkinode(m, md, false, # links(m, dirs), 0, m1), buf0, buf0, 0, dirs, files), fd ∈ of, m ∈ files, m0 + n ≤ m1, m0 ≤ m1, n0 ≤ # buf0, n ≤ # buf0, n ≤ n0, psynced → asynced, ⌊err1⌋ ∨ err1 = ESUCCESS ⊦ ino = 0, mode ≠ MODE_R ∧ mode ≠ MODE_RW, m0 + ino ≤ m1 ∧ ino ≤ # buf0

Rule argument

Additional information

Used simplifier rules: ⊦ ⌜m⌝ < ∞; (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)% ⊦ ⌜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)