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Proof step 30 from proof valid-content-reduce (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ valid-content(ino, files) ↔ (∀ n. n ∈ files[ino].content → n * VFS_PAGE_SIZE < files[ino].size)
Proof step 32:
files0[ino] = mkfile(m1, md0, m2, content0), files1[ino] = mkfile(m, md, m0, content), n ∈ content, ino ∈ files1, ino ∈ files0, n ∈ content0, m ≤ n * VFS_PAGE_SIZE, m1 ≤ n * VFS_PAGE_SIZE, ∀ n. n ∈ files0[ino].content → n * VFS_PAGE_SIZE < files0[ino].size ⊦

Rule argument

spec: afs-base name: valid-content seq: ⊦ valid-content(ino, files) ↔ (∀ n. n ∈ files[ino].content → n * VFS_PAGE_SIZE < files[ino].size) subst: [files, ino] → [files0, ino] flags: <all paths>

Additional information

Used terms: files0, ino