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Proof step 69 from proof truncate-greater (previous step)

files0[m0] = mkfile(m, md0, # links(m0, dirs), content0), afs-cons(dirs, files0), m1 ∈ content0, m0 ∈ files0 ⊦ [asynced := ?] ( ((content0.stream to m1 * (n0 + n2) + n2) + (σ⊥ to n0 to n0)) + σ⊥ to n1 + m1 * (n0 + n2) + n2 = (content0.stream to m1 * (n0 + n2) + n2) + (σ⊥ to n1)), n0 = 0, n1 = 0, n2 = 0, #(σ⊥ to n0) < ⌜n0⌝ , # content0.stream < ⌜m1 * (n0 + n2) + n2⌝

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 70:
files0[m0] = mkfile(m, md0, # links(m0, dirs), content0), n0 ≠ 0, n1 ≠ 0, n2 ≠ 0, afs-cons(dirs, files0), m0 ∈ files0, m1 ∈ content0 ⊦ [asynced := ?] ((content0.stream to m1 * (n0 + n2) + n2) + (σ⊥ to n0) + σ⊥ to n1 + m1 * (n0 + n2) + n2 = (content0.stream to m1 * (n0 + n2) + n2) + (σ⊥ to n1))

Rule argument

Additional information

Used simplifier rules: append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf]%¬ # σ0 < ⌜n⌝ ⊦ σ0 to n to n = σ0 to n; (s)% ⊦ m ≤ m; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; (s)%¬ # σ0 < ⌜n⌝ ⊦ #(σ0 to n) = ⌜n⌝ ; (s)% ⊦ # σ⊥ = ∞; (s)% ⊦ ¬ ∞ < n∞; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ ; (s)% ⊦ # content.stream = ∞; (s)