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Proof step 1 from proof upto-stream (conclusion)

⊦ (content upto m).stream to m = content.stream to m

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ (λ n. (n / VFS_PAGE_SIZE * VFS_PAGE_SIZE < m ∧ n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) to m = (λ n. (n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) to m

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)%⊦ m * VFS_PAGE_SIZE < n ∧ m ∈ content → (content upto n)[m] = content[m]; (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ m ∈ content upto n ↔ m * VFS_PAGE_SIZE < n ∧ m ∈ content; (s)