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Proof step 573 from proof inv-write (previous step)

of[n0] = mkfile(m2, mode0, m3), files0[m] = mkfile(m1, md, # links(m, dirs), content0), of[fd] = mkfile(m, mode, m0), of[fd, mkfile(m, mode, m0 + (m0 ≤ m1 ⊃ m1 - m0;0))][n0] = mkfile(m4, mode1, m5), dom of < ino3, m1 < m0 + ino4, afs-cons(dirs, files0), afs-cons(dirs, files), of-cons(of, dirs, files0), of-cons(of, dirs, files), n0 ∈ of, m2 ∈ files0, fd ∈ of, m ∈ files0, n0 ∈ of[fd, mkfile(m, mode, m0 + (m1 - m0))], n ≤ # buf0, ⌊err0⌋ ⊦ ino4 = 0, n = 0, m4 ∈ files, mode ≠ MODE_W ∧ mode ≠ MODE_RW, m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0, err1 = ESUCCESS ∧ ¬ isdir

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 574:
of[fd, mkfile(m, mode, m0 + (m0 ≤ m1 ⊃ n1;0))][n0] = mkfile(m4, mode1, m5), of[fd] = mkfile(m, mode, m0), files0[m] = mkfile(m1, md, # links(m, dirs), content0), of[n0] = mkfile(m2, mode0, m3), m1 = n1 + m0, m1 < m0 + ino4, dom of < ino3, afs-cons(dirs, files), afs-cons(dirs, files0), of-cons(of, dirs, files), of-cons(of, dirs, files0), n0 ∈ of[fd, mkfile(m, mode, m0 + n1)], m ∈ files0, fd ∈ of, m2 ∈ files0, n0 ∈ of, n ≤ # buf0, m0 ≤ m1, ⌊err0⌋ ⊦ ino4 = 0, n = 0, m4 ∈ files, err1 = ESUCCESS ∧ ¬ isdir, m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [m0, m1, n1]

Additional information

Used simplifier rules: ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ of[fd] = file ∧ fd ∈ of → of[fd, file] = of; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%⊦ of-cons(of, dirs, files) ∧ fd ∈ of ∧ of[fd] = mkfile(ino, mode, n) → ino ∈ files; (ss)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: m0, m1, n1