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Proof step 5 from proof upto-less (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
n ≤ m ⊦ (n0 * VFS_PAGE_SIZE < n ∧ n0 ∈ content → n0 * VFS_PAGE_SIZE < m) ∧ (n0 * VFS_PAGE_SIZE < n ∧ n0 * VFS_PAGE_SIZE < m ∧ n0 ∈ content → ((content upto m) 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];%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult