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Proof step 66 from proof truncate-greater (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 67:
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) to (n0 + n2) * m1 + n0 + n2) + σ⊥ to n1 + m1 * (n0 + n2) + n2 = (content0.stream to m1 * (n0 + n2) + n2) + (σ⊥ to n1))

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < m + n ↔ n ≠ 0; (s)