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Proof step 5 from proof iso-sym (previous step)

files0 ~ files1 ⊦ ∀ ino. (ino ∈ files1 ↔ ino ∈ files0) ∧ ( ino ∈ files1 → files1[ino].size = files0[ino].size ∧ files1[ino].meta = files0[ino].meta ∧ files1[ino].nlink = files0[ino].nlink ∧ files1[ino].content.stream to files1[ino].size = files0[ino].content.stream to files0[ino].size)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
files0 ~ files1 ⊦ (ino ∈ files1 ↔ ino ∈ files0) ∧ ( ino ∈ files1 → files1[ino].size = files0[ino].size ∧ files1[ino].meta = files0[ino].meta ∧ files1[ino].nlink = files0[ino].nlink ∧ (λ n. (n / VFS_PAGE_SIZE ∈ files1[ino].content ⊃ files1[ino].content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) to files1[ino].size = (λ n. (n / VFS_PAGE_SIZE ∈ files0[ino].content ⊃ files0[ino].content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) to files0[ino].size)

Rule argument

Additional information

Used simplifier rules: stream: ⊦ content.stream = ⌜λ n. getbyte(n, content)⌝ ;%getbyte: ⊦ getbyte(m, content) = getpage(m / VFS_PAGE_SIZE, content)[m % VFS_PAGE_SIZE];%getpage: ⊦ getpage(n, content) = (n ∈ content ⊃ content[n];zeropage);% ⊦ ⌜dx⌝ = ⌜dx0⌝ ↔ dx = dx0; (s)% ⊦ ⌜nf0⌝ to n = ⌜nf0 to n⌝ ; (s)