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Proof step 4 from proof upto-idem (previous step)

n0 * VFS_PAGE_SIZE < n, n0 ∈ content ⊦ ((content upto n) upto n)[n0] = content[n0]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ m * VFS_PAGE_SIZE < n ∧ m ∈ content → (content upto n)[m] = content[m]

Rule argument

spec: <toplevel> name: at-upto seq: ⊦ m * VFS_PAGE_SIZE < n ∧ m ∈ content → (content upto n)[m] = content[m] subst: [m, n, content] → [n0, n, content upto n] flags: <all paths>

Additional information

Used simplifier rules: in-upto: ⊦ m ∈ content upto n ↔ m * VFS_PAGE_SIZE < n ∧ m ∈ content;%at-upto: ⊦ m * VFS_PAGE_SIZE < n ∧ m ∈ content → (content upto n)[m] = content[m];%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult Used terms: n0, n, content upto n