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Proof step 9 from proof iso-sym (previous step)

files1[ino] = mkfile(m, md, m0, content), files0[ino] = mkfile(m1, md0, m2, content0), files0 ~ files1 ⊦ (ino ∈ files1 ↔ ino ∈ files0) ∧ ( ino ∈ files1 → m = m1 ∧ md = md0 ∧ m0 = m2 ∧ (λ n. (n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) to m1 = (λ n. (n / VFS_PAGE_SIZE ∈ content0 ⊃ content0[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) to m1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ files0 ~ files1 ↔ (∀ ino. (ino ∈ files0 ↔ ino ∈ files1) ∧ ( ino ∈ files0 → files0[ino].size = files1[ino].size ∧ files0[ino].meta = files1[ino].meta ∧ files0[ino].nlink = files1[ino].nlink ∧ files0[ino].content.stream to files0[ino].size = files1[ino].content.stream to files1[ino].size))
Proof step 11:
files0[ino] = mkfile(m1, md0, m2, content0), files1[ino] = mkfile(m, md, m0, content), ∀ ino. (ino ∈ files0 ↔ ino ∈ files1) ∧ ( ino ∈ files0 → files0[ino].size = files1[ino].size ∧ files0[ino].meta = files1[ino].meta ∧ files0[ino].nlink = files1[ino].nlink ∧ files0[ino].content.stream to files0[ino].size = files1[ino].content.stream to files1[ino].size) ⊦ (ino ∈ files1 ↔ ino ∈ files0) ∧ ( ino ∈ files1 → m = m1 ∧ md = md0 ∧ m0 = m2 ∧ (λ n. (n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) to m1 = (λ n. (n / VFS_PAGE_SIZE ∈ content0 ⊃ content0[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) to m1)

Rule argument

spec: <toplevel> name: files-iso seq: ⊦ files0 ~ files1 ↔ (∀ ino. (ino ∈ files0 ↔ ino ∈ files1) ∧ ( ino ∈ files0 → files0[ino].size = files1[ino].size ∧ files0[ino].meta = files1[ino].meta ∧ files0[ino].nlink = files1[ino].nlink ∧ files0[ino].content.stream to files0[ino].size = files1[ino].content.stream to files1[ino].size)) subst: [files1, files0] → [files1, files0] flags: <all paths>

Additional information

Used terms: files1, files0