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Proof step 50 from proof truncate-smaller (previous step)

VFS_PAGE_SIZE = n0 + n1, files0[m] = mkfile(m0, md0, # links(m, dirs), content0), n1 < VFS_PAGE_SIZE, afs-cons(dirs, files0), m ∈ files0, m1 ∈ content0 ⊦ [asynced := ?] ( (content0.stream to m1 * VFS_PAGE_SIZE) + (((content0.stream from m1 * VFS_PAGE_SIZE) to n1) + (σ⊥ to n0) + (content0.stream from VFS_PAGE_SIZE * m1 + VFS_PAGE_SIZE) to n1) = content0.stream to m1 * VFS_PAGE_SIZE + n1), n0 = 0, n1 = 0, #(((content0.stream from m1 * VFS_PAGE_SIZE) to n1) + (σ⊥ to n0) + (content0.stream from VFS_PAGE_SIZE * m1 + VFS_PAGE_SIZE)) < ⌜n1⌝ , # content0.stream < ⌜m1 * VFS_PAGE_SIZE⌝

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 51:
VFS_PAGE_SIZE = n0 + n1, files0[m] = mkfile(m0, md0, # links(m, dirs), content0), n0 ≠ 0, n1 ≠ 0, n1 < VFS_PAGE_SIZE, afs-cons(dirs, files0), m1 ∈ content0, m ∈ files0 ⊦ [asynced := ?] ( (content0.stream to m1 * VFS_PAGE_SIZE) + (((content0.stream from m1 * VFS_PAGE_SIZE) to n1) + (σ⊥ to n0) + (content0.stream from VFS_PAGE_SIZE * m1 + VFS_PAGE_SIZE) to n1) = content0.stream to m1 * VFS_PAGE_SIZE + n1)

Rule argument

Additional information

Used simplifier rules: append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf]%add-comm: ⊦ n∞1 + n∞2 = n∞2 + n∞1; from specification nat-inf%add-assoc: ⊦ (n∞ + n∞1) + n∞2 = n∞ + n∞1 + n∞2; from specification nat-inf% ⊦ ⌜m⌝ + ∞ = ∞; (s)% ⊦ # σ⊥ = ∞; (s)%¬ # σ0 < ⌜n⌝ ⊦ #(σ0 to n) = ⌜n⌝ ; (s)% ⊦ #(content.stream from n) = ∞; (s)% ⊦ #(σ0 + σ2) = # σ0 + # σ2; (s)% ⊦ ¬ ∞ < n∞; (s)% ⊦ # content.stream = ∞; (s)