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Proof step 202 from proof refine-read (previous step)

of[fd] = mkfile(m3, mode0, m4), files[m3] = mkfile(m1, md, m2, 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), read-inv(m4, m4 + n, mkinode(m3, md, false, m2, 0, m1), buf0, buf1, 0, dirs, files), read-inv(m4, m4 + n, mkinode(m3, md, false, m2, 0, m1), buf0, buf0, 0, dirs, files), fd ∈ of, m4 ≤ m1, n ≤ # buf0, ⌊err1⌋ , psynced → asynced ⊦ buf1 = buf0, mode0 ≠ MODE_R ∧ mode0 ≠ MODE_RW

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 203:
⊦ read-inv(n0, n1, inode, buf0, buf1, n, dirs, files) ↔ afs-cons(dirs, files) ∧ # buf0 = # buf1 ∧ inode.ino ∈ files ∧ files[inode.ino].size = inode.size ∧ n0 + n ≤ n1 ∧ n0 + n ≤ inode.size ∧ n1 - n0 ≤ # buf0 ∧ read-inv(n0, n1, buf0, buf1, n, files[inode.ino].content)
Proof step 204:
# buf0 = # buf1, files[mkinode(m3, md, false, m2, 0, m1).ino].size = mkinode(m3, md, false, m2, 0, m1).size, files[m3] = mkfile(m1, md, m2, content), of[fd] = mkfile(m3, mode0, m4), 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), read-inv(m4, m4 + n, mkinode(m3, md, false, m2, 0, m1), buf0, buf0, 0, dirs, files), read-inv(m4, m4 + n, buf0, buf1, 0, files[mkinode(m3, md, false, m2, 0, m1).ino].content), fd ∈ of, mkinode(m3, md, false, m2, 0, m1).ino ∈ files, n ≤ # buf0, m4 ≤ m1, m4 + 0 ≤ m4 + n, m4 + 0 ≤ mkinode(m3, md, false, m2, 0, m1).size, m4 + n - m4 ≤ # buf0, ⌊err1⌋ , psynced → asynced ⊦ buf1 = buf0, mode0 ≠ MODE_R ∧ mode0 ≠ MODE_RW

Rule argument

spec: vfs-contracts name: read-inv-strong seq: ⊦ read-inv(n0, n1, inode, buf0, buf1, n, dirs, files) ↔ afs-cons(dirs, files) ∧ # buf0 = # buf1 ∧ inode.ino ∈ files ∧ files[inode.ino].size = inode.size ∧ n0 + n ≤ n1 ∧ n0 + n ≤ inode.size ∧ n1 - n0 ≤ # buf0 ∧ read-inv(n0, n1, buf0, buf1, n, files[inode.ino].content) subst: [files, dirs, n, buf1, buf0, inode, n1, n0] → [files, dirs, 0, buf1, buf0, mkinode(m3, md, false, m2, 0, m1), m4 + n, m4] flags: <all paths>

Additional information

Used terms: files, dirs, 0, buf1, buf0, mkinode(m3, md, false, m2, 0, m1), m4 + n, m4