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Proof step 7 from proof upto-same (previous step)

files[ino] = mkfile(m0, md0, m1, content0), ino ∈ files, ∀ n. n ∈ content0 → n * VFS_PAGE_SIZE < m0 ⊦ ∀ n. (n ∈ content0 upto m0 ↔ n ∈ content0) ∧ (n ∈ content0 upto m0 → (content0 upto m0)[n] = content0[n])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
files[ino] = mkfile(m0, md0, m1, content0), ino ∈ files, n ∈ content0, m0 ≤ n * VFS_PAGE_SIZE, ∀ n. n ∈ content0 → n * VFS_PAGE_SIZE < m0 ⊦

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 ≤ m; (ss)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult