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Proof step 6 from proof content-write (previous step)

# buf = VFS_PAGE_SIZE ⊦ (n0 / VFS_PAGE_SIZE ∈ content[n, buf] ⊃ content[n, buf][n0 / VFS_PAGE_SIZE];zeropage)[n0 % VFS_PAGE_SIZE] = ( ⌜(λ n. (n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) to n * VFS_PAGE_SIZE⌝ + ⌜buf⌝ + ⌜(λ n. (n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) from VFS_PAGE_SIZE * n + VFS_PAGE_SIZE⌝ )[n0 ]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ n ∈ content[n0, buf] ↔ n = n0 ∨ n ∈ content
Proof step 8:
# buf = VFS_PAGE_SIZE ⊦ (n0 / VFS_PAGE_SIZE = n ∨ n0 / VFS_PAGE_SIZE ∈ content ⊃ content[n, buf][n0 / VFS_PAGE_SIZE];zeropage)[n0 % VFS_PAGE_SIZE] = ( ⌜(λ n. (n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) to n * VFS_PAGE_SIZE⌝ + ⌜buf⌝ + ⌜(λ n. (n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) from VFS_PAGE_SIZE * n + VFS_PAGE_SIZE⌝ )[n0 ]

Rule argument

spec: store, inst: file-content name: In-insert seq: ⊦ n ∈ content[n0, buf] ↔ n = n0 ∨ n ∈ content subst: [buf, n0, content, n] → [buf, n, content, n0 / VFS_PAGE_SIZE] flags: <all paths>

Additional information

Used terms: buf, n, content, n0 / VFS_PAGE_SIZE