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Proof step 4 from proof getbyte-drop-upper (previous step)

n / VFS_PAGE_SIZE ∈ content[m, buf], VFS_PAGE_SIZE * m + VFS_PAGE_SIZE ≤ n ⊦ content[m, buf][n / VFS_PAGE_SIZE][n % VFS_PAGE_SIZE] = (n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ n ≠ n0 → content[n0, buf][n] = content[n]
Proof step 6:
n / VFS_PAGE_SIZE = m, n / VFS_PAGE_SIZE ∈ content[m, buf], VFS_PAGE_SIZE * m + VFS_PAGE_SIZE ≤ n ⊦ content[m, buf][n / VFS_PAGE_SIZE][n % VFS_PAGE_SIZE] = (n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]

Rule argument

spec: store, inst: file-content name: At-other seq: ⊦ n ≠ n0 → content[n0, buf][n] = content[n] subst: [n, buf, n0, content] → [n / VFS_PAGE_SIZE, buf, m, content] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n ≠ n0 → (n ∈ content[n0, buf] ↔ n ∈ content); (s) Used terms: n / VFS_PAGE_SIZE, buf, m, content