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Proof step 571 from proof inv-write (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 572:
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), fd ∈ of, m ∈ files0, n0 ∈ of[fd, mkfile(m, mode, m0 + (m0 ≤ m1 ⊃ m1 - m0;0))], n0 ∈ of, m2 ∈ files0, 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

Rule argument

spec: file name: elim seq: ⊦ (m = file.ino ∧ mode = file.mode) ∧ m0 = file.pos ↔ file = mkfile(m, mode, m0) subst: [file, m, mode, m0] → [of[fd, mkfile(m, mode, m0 + (m0 ≤ m1 ⊃ m1 - m0;0))][n0], m4, mode1, m5]

Additional information

Used simplifier rules: ⊦ (m = file.ino ∧ mode = file.mode) ∧ m0 = file.pos ↔ file = mkfile(m, mode, m0); (elim) Used terms: of[fd, mkfile(m, mode, m0 + (m0 ≤ m1 ⊃ m1 - m0;0))][n0], m4, mode1, m5