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Proof step 284 from proof inv-write (previous step)

m1 + n1 = m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE + VFS_PAGE_SIZE, files1[m] = mkfile(m1, md0, # links(m, dirs), content0), of[fd] = mkfile(m, mode, m0), files[m] = mkfile(m2, md, # links(m, dirs), content), m1 = n2 + m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, m1 < m0 + ino4, dom of < ino3, afs-cons(dirs, files1), afs-cons(dirs, files), of-cons(of, dirs, files1), of-cons(of, dirs, files), m ∈ files, fd ∈ of, m1 / VFS_PAGE_SIZE ∈ content0, m ∈ files1, n0 ∈ of[fd, mkfile(m, mode, m0 + (m0 ≤ m1 ⊃ m1 - m0;0))], n0 ∈ of, of[n0].ino ∈ files1, n2 + n1 ≤ VFS_PAGE_SIZE, n ≤ # buf0, m1 % VFS_PAGE_SIZE + n1 ≤ VFS_PAGE_SIZE, ⌊err0⌋ ⊦ ino4 = 0, n = 0, n2 = 0, of[fd, mkfile(m, mode, m0 + (m0 ≤ m1 ⊃ m1 - m0;0))][n0].ino ∈ files, mode ≠ MODE_W ∧ mode ≠ MODE_RW, err1 = ESUCCESS ∧ ¬ isdir

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 285:
m1 + n1 = m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE + VFS_PAGE_SIZE, files[m] = mkfile(m2, md, # links(m, dirs), content), of[fd] = mkfile(m, mode, m0), files1[m] = mkfile(m1, md0, # links(m, dirs), content0), of[n0] = mkfile(m3, mode0, m4), m1 = n2 + m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, dom of < ino3, m1 < m0 + ino4, afs-cons(dirs, files), afs-cons(dirs, files1), of-cons(of, dirs, files), of-cons(of, dirs, files1), m3 ∈ files1, n0 ∈ of, n0 ∈ of[fd, mkfile(m, mode, m0 + (m0 ≤ m1 ⊃ m1 - m0;0))], m ∈ files1, m1 / VFS_PAGE_SIZE ∈ content0, fd ∈ of, m ∈ files, m1 % VFS_PAGE_SIZE + n1 ≤ VFS_PAGE_SIZE, n ≤ # buf0, n2 + n1 ≤ VFS_PAGE_SIZE, ⌊err0⌋ ⊦ ino4 = 0, n = 0, n2 = 0, of[fd, mkfile(m, mode, m0 + (m0 ≤ m1 ⊃ m1 - m0;0))][n0].ino ∈ files, err1 = ESUCCESS ∧ ¬ isdir, mode ≠ MODE_W ∧ mode ≠ MODE_RW

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[n0], m3, mode0, m4]

Additional information

Used simplifier rules: ⊦ (m = file.ino ∧ mode = file.mode) ∧ m0 = file.pos ↔ file = mkfile(m, mode, m0); (elim) Used terms: of[n0], m3, mode0, m4