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Proof step 9 from proof valid-content-reduce (previous step)

files1[ino] = mkfile(m, md, m0, content), files0[ino] = mkfile(m1, md0, m2, content0), valid-content(files1), ino ∈ files1, n ∈ content, m ≤ n * VFS_PAGE_SIZE, ino ∈ files0 ∧ n ∈ content0 → n * VFS_PAGE_SIZE < m1, ∀ ino. ino ∈ files0 → valid-content(ino, files0) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ valid-content(files) ↔ (∀ ino. ino ∈ files → valid-content(ino, files))
Proof step 11:
files0[ino] = mkfile(m1, md0, m2, content0), files1[ino] = mkfile(m, md, m0, content), n ∈ content, ino ∈ files1, m ≤ n * VFS_PAGE_SIZE, ino ∈ files0 ∧ n ∈ content0 → n * VFS_PAGE_SIZE < m1, ∀ ino. ino ∈ files0 → valid-content(ino, files0), ∀ ino. ino ∈ files1 → valid-content(ino, files1) ⊦

Rule argument

spec: vfs-base name: valid-content seq: ⊦ valid-content(files) ↔ (∀ ino. ino ∈ files → valid-content(ino, files)) subst: [files] → [files1] flags: <all paths>

Additional information

Used terms: files1