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Proof step 7 from proof write-inv-stream (previous step)

files1[ino] = mkfile(m1, md1, n3, content1), files0[ino] = mkfile(m1, md1, n2, content0), write-inv(n0, n1, mkinode(ino, md, false, m, m3, m2), buf, n, dirs, files0, files1), ino ∈ files1 ⊦ content1.stream = (content0.stream to n0) + (⌜buf⌝ to n) + (content0.stream from n0 + n)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ write-inv(n0, n1, inode, buf, n, dirs, files0, files1) ↔ afs-cons(dirs, files1) ∧ inode.ino ∈ files0 ∧ inode.ino ∈ files1 ∧ files0[inode.ino].size = inode.size ∧ files1[inode.ino].size = files0[inode.ino].size ∧ files1[inode.ino].meta = files0[inode.ino].meta ∧ files1 -- inode.ino = files0 -- inode.ino ∧ n0 + n ≤ n1 ∧ n1 - n0 ≤ # buf ∧ write-inv(n0, n1, buf, n, files0[inode.ino].content, files1[inode.ino].content)
Proof step 9:
files1 -- mkinode(ino, md, false, m, m3, m2).ino = files0 -- mkinode(ino, md, false, m, m3, m2).ino, files1[mkinode(ino, md, false, m, m3, m2).ino].meta = files0[mkinode(ino, md, false, m, m3, m2).ino].meta, files0[mkinode(ino, md, false, m, m3, m2).ino].size = mkinode(ino, md, false, m, m3, m2).size, files1[mkinode(ino, md, false, m, m3, m2).ino].size = files0[mkinode(ino, md, false, m, m3, m2).ino].size, files0[ino] = mkfile(m1, md1, n2, content0), files1[ino] = mkfile(m1, md1, n3, content1), afs-cons(dirs, files1), write-inv(n0, n1, buf, n, files0[mkinode(ino, md, false, m, m3, m2).ino].content, files1[mkinode(ino, md, false, m, m3, m2).ino].content), ino ∈ files1, mkinode(ino, md, false, m, m3, m2).ino ∈ files0, mkinode(ino, md, false, m, m3, m2).ino ∈ files1, n0 + n ≤ n1, n1 - n0 ≤ # buf ⊦ content1.stream = (content0.stream to n0) + (⌜buf⌝ to n) + (content0.stream from n0 + n)

Rule argument

spec: <toplevel> name: write-inv-strong seq: ⊦ write-inv(n0, n1, inode, buf, n, dirs, files0, files1) ↔ afs-cons(dirs, files1) ∧ inode.ino ∈ files0 ∧ inode.ino ∈ files1 ∧ files0[inode.ino].size = inode.size ∧ files1[inode.ino].size = files0[inode.ino].size ∧ files1[inode.ino].meta = files0[inode.ino].meta ∧ files1 -- inode.ino = files0 -- inode.ino ∧ n0 + n ≤ n1 ∧ n1 - n0 ≤ # buf ∧ write-inv (n0, n1, buf, n, files0[inode.ino].content, files1[inode.ino].content) subst: [files1, files0, dirs, n, buf, inode, n1, n0] → [files1, files0, dirs, n, buf, mkinode(ino, md, false, m, m3, m2), n1, n0] flags: <all paths>

Additional information

Used terms: files1, files0, dirs, n, buf, mkinode(ino, md, false, m, m3, m2), n1, n0