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Proof step 3 from proof upto-idem (previous step)

⊦ ∀ n0. (n0 ∈ (content upto n) upto n ↔ n0 ∈ content upto n) ∧ (n0 ∈ (content upto n) upto n → ((content upto n) upto n)[n0] = (content upto n)[n0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
n0 * VFS_PAGE_SIZE < n, n0 ∈ content ⊦ ((content upto n) upto n)[n0] = content[n0]

Rule argument

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];% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult