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Proof step 102 from proof inv-write (previous step)

m1 + n1 = m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE + VFS_PAGE_SIZE, files1[m] = mkfile(m1, md, # links(m, dirs), content0), of[fd] = mkfile(m, mode, m0), err = ESUCCESS, m1 = n2 + m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, min(n0 - ino0, VFS_PAGE_SIZE - (m0 + ino0) % VFS_PAGE_SIZE) ≠ 0, n0 ≠ 0, n2 ≠ 0, dom of < ino3, afs-cons(dirs, files1), afs-cons(dirs, files), of-cons(of, dirs, files1), of-cons(of, dirs, files), fd ∈ of, m1 / VFS_PAGE_SIZE ∈ content0, m ∈ files1, n2 + n1 ≤ VFS_PAGE_SIZE, n0 ≤ # buf0, ino0 ≤ n0, ino0 ≤ # buf0 ⊦ [vfs_writepage# (mkinode(m, md, false, # links(m, dirs), 0, m1), (m0 + ino0) / VFS_PAGE_SIZE, buf0, ino0, (m0 + ino0) % VFS_PAGE_SIZE, min(m0 + n0 - m0 + ino0, VFS_PAGE_SIZE - (m0 + ino0) % VFS_PAGE_SIZE), dirs ; err, files, asynced); if err = ESUCCESS then ino3 := ino0 + min(m0 + n0 - m0 + ino0, VFS_PAGE_SIZE - (m0 + ino0) % VFS_PAGE_SIZE)] (of-cons(of, dirs, files) ∧ afs-cons(dirs, files)), mode ≠ MODE_W ∧ mode ≠ MODE_RW

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 103:
m1 + n1 = m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE + VFS_PAGE_SIZE, VFS_PAGE_SIZE = n3 + (m0 + ino0) % VFS_PAGE_SIZE, of[fd] = mkfile(m, mode, m0), files1[m] = mkfile(m1, md, # links(m, dirs), content0), err = ESUCCESS, m1 = n2 + m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, dom of < ino3, afs-cons(dirs, files), afs-cons(dirs, files1), of-cons(of, dirs, files), of-cons(of, dirs, files1), m ∈ files1, m1 / VFS_PAGE_SIZE ∈ content0, fd ∈ of, ino0 ≤ # buf0, ino0 ≤ n0, n0 ≤ # buf0, n2 + n1 ≤ VFS_PAGE_SIZE, (m0 + ino0) % VFS_PAGE_SIZE ≤ VFS_PAGE_SIZE ⊦ [vfs_writepage# (mkinode(m, md, false, # links(m, dirs), 0, m1), (m0 + ino0) / VFS_PAGE_SIZE, buf0, ino0, (m0 + ino0) % VFS_PAGE_SIZE, min(m0 + n0 - m0 + ino0, n3), dirs ; err, files, asynced); if err = ESUCCESS then ino3 := ino0 + min(m0 + n0 - m0 + ino0, n3)] (of-cons(of, dirs, files) ∧ afs-cons(dirs, files)), min(n0 - ino0, n3) = 0, n0 = 0, n2 = 0, 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 + ino0) % VFS_PAGE_SIZE, VFS_PAGE_SIZE, n]

Additional information

Used simplifier rules: ⊦ VFS_PAGE_SIZE ≠ 0; (s)%n ≠ 0 ⊦ m % n ≤ n; (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: (m0 + ino0) % VFS_PAGE_SIZE, VFS_PAGE_SIZE, n