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Proof step 6 from proof stream-split-lastpage (previous step)

n < VFS_PAGE_SIZE + m * VFS_PAGE_SIZE ⊦ (n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE] = (⌜(λ n. (n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) to m * VFS_PAGE_SIZE⌝ + (σ⊥ to VFS_PAGE_SIZE))[n], m ∈ content

User applied rule case distinction

And obtained the following new goals

Proof step 7:
n < VFS_PAGE_SIZE + m * VFS_PAGE_SIZE, n / VFS_PAGE_SIZE ∈ content ⊦ content[n / VFS_PAGE_SIZE][n % VFS_PAGE_SIZE] = (⌜(λ n. (n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) to m * VFS_PAGE_SIZE⌝ + (σ⊥ to VFS_PAGE_SIZE))[n], m ∈ content
Proof step 12:
n < VFS_PAGE_SIZE + m * VFS_PAGE_SIZE ⊦ (zeropage)[n % VFS_PAGE_SIZE] = (⌜(λ n. (n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) to m * VFS_PAGE_SIZE⌝ + (σ⊥ to VFS_PAGE_SIZE))[n], m ∈ content, n / VFS_PAGE_SIZE ∈ content

Rule argument

pos: right 1

Proof step 6 from proof stream-split-lastpage (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information