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Proof step 112 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, m0 + ino ≤ m1, mode ≠ MODE_R ∧ mode ≠ MODE_RW

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 113:
files[m] = mkfile(m1, md, # links(m, dirs), content), of[fd] = mkfile(m, mode, m0), root.dir?, n < ino, dom of < ino2, m1 < m0 + ino, 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 ⊦ mode ≠ MODE_R ∧ mode ≠ MODE_RW

Rule argument

Additional information

Used simplifier rules: ⊦ m + n < m + n0 ↔ n < n0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < m + n ↔ n ≠ 0; (s)% ⊦ m < n → n ≠ 0; (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)