[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 11 from proof iso-trans (previous step)

files2[ino] = mkfile(m1, md0, m2, content0), files0[ino] = mkfile(m, md, m0, content), files0 ~ files1, ∀ ino. (ino ∈ files1 ↔ ino ∈ files2) ∧ ( ino ∈ files1 → files1[ino].size = files2[ino].size ∧ files1[ino].meta = files2[ino].meta ∧ files1[ino].nlink = files2[ino].nlink ∧ files1[ino].content.stream to files1[ino].size = files2[ino].content.stream to files2[ino].size) ⊦ (ino ∈ files0 ↔ ino ∈ files2) ∧ ( ino ∈ files0 → 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 12:
⊦ 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 13:
files0[ino] = mkfile(m, md, m0, content), files2[ino] = mkfile(m1, md0, m2, content0), ∀ ino. (ino ∈ files1 ↔ ino ∈ files2) ∧ ( ino ∈ files1 → files1[ino].size = files2[ino].size ∧ files1[ino].meta = files2[ino].meta ∧ files1[ino].nlink = files2[ino].nlink ∧ files1[ino].content.stream to files1[ino].size = files2[ino].content.stream to files2[ino].size), ∀ 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 ∈ files0 ↔ ino ∈ files2) ∧ ( ino ∈ files0 → 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