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

n0 < n + m * VFS_PAGE_SIZE, n < VFS_PAGE_SIZE ⊦ (n0 / VFS_PAGE_SIZE ∈ content ⊃ content[n0 / VFS_PAGE_SIZE];zeropage)[n0 % VFS_PAGE_SIZE] = (⌜(λ n0. (n0 / VFS_PAGE_SIZE ∈ content ⊃ content[n0 / VFS_PAGE_SIZE];zeropage)[n0 % VFS_PAGE_SIZE]) to m * VFS_PAGE_SIZE⌝ + (σ⊥ to n))[n0], m ∈ content

User applied rule case distinction

And obtained the following new goals

Proof step 7:
n < VFS_PAGE_SIZE, n0 < n + m * VFS_PAGE_SIZE, n0 / VFS_PAGE_SIZE ∈ content ⊦ content[n0 / VFS_PAGE_SIZE][n0 % VFS_PAGE_SIZE] = (⌜(λ n0. (n0 / VFS_PAGE_SIZE ∈ content ⊃ content[n0 / VFS_PAGE_SIZE];zeropage)[n0 % VFS_PAGE_SIZE]) to m * VFS_PAGE_SIZE⌝ + (σ⊥ to n))[n0], m ∈ content
Proof step 12:
n < VFS_PAGE_SIZE, n0 < n + m * VFS_PAGE_SIZE ⊦ (zeropage)[n0 % VFS_PAGE_SIZE] = (⌜(λ n0. (n0 / VFS_PAGE_SIZE ∈ content ⊃ content[n0 / VFS_PAGE_SIZE];zeropage)[n0 % VFS_PAGE_SIZE]) to m * VFS_PAGE_SIZE⌝ + (σ⊥ to n))[n0], m ∈ content, n0 / VFS_PAGE_SIZE ∈ content

Rule argument

pos: right 1

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

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information