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Proof step 70 from proof truncate-greater (previous step)

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))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: stream, inst: buffer-inf name: to-append-add seq: ⊦ ¬ # σ1 < ⌜n⌝ ∧ ¬ # σ2 < ⌜n1⌝ → (σ1 to n) + σ2 to n1 + n = (σ1 to n) + (σ2 to n1) subst: [n1, σ2, n, σ1] → [n1, (σ⊥ to n0) + σ⊥, m1 * (n0 + n2) + n2, content0.stream] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # content.stream = ∞; (s)% ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ ; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ ¬ ∞ < n∞; (s)% ⊦ #(σ0 + σ2) = # σ0 + # σ2; (s)% ⊦ # σ⊥ = ∞; (s)%¬ # σ0 < ⌜n⌝ ⊦ #(σ0 to n) = ⌜n⌝ ; (s)% ⊦ ⌜m⌝ + ∞ = ∞; (s)%add-assoc: ⊦ (n∞ + n∞1) + n∞2 = n∞ + n∞1 + n∞2; from specification nat-inf%add-comm: ⊦ n∞1 + n∞2 = n∞2 + n∞1; from specification nat-inf%append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf]% ⊦ (σ⊥ to n) + σ⊥ to m = σ⊥ to m; (s)% ⊦ n∞ < ∞ ↔ n∞ ≠ ∞; (s)% ⊦ ⌜m⌝ + n∞ = ∞ ↔ n∞ = ∞; (s)% ⊦ ⌜m⌝ ≠ ∞; (s)% ⊦ ⌜m⌝ < ∞; (s) Used terms: n1, (σ⊥ to n0) + σ⊥, m1 * (n0 + n2) + n2, content0.stream