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Proof step 2 from proof getbyte-drop-upper (previous step)

(m + 1) * VFS_PAGE_SIZE ≤ n ⊦ getbyte(n, content[m, buf]) = getbyte(n, content)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
VFS_PAGE_SIZE * m + VFS_PAGE_SIZE ≤ n ⊦ (n / VFS_PAGE_SIZE ∈ content[m, buf] ⊃ content[m, buf][n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE] = (n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]

Rule argument

Additional information

Used simplifier rules: getbyte: ⊦ getbyte(m, content) = getpage(m / VFS_PAGE_SIZE, content)[m % VFS_PAGE_SIZE];%getpage: ⊦ getpage(n, content) = (n ∈ content ⊃ content[n];zeropage);%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m * (n + 1) = m * n + m; (s)