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Proof step 53 from proof swap-to-from-app (previous step)

⌜x⌝ = (σ to n0 + m) + σ0 ⊦ ⌜n0⌝ + # σ0 = ⌜0⌝ , ⌜((⌜n0⌝ + ⌜m⌝ ) + # σ0).n - m⌝ = #((σ to m + n0) from m) + # σ0, # σ < ⌜m⌝ + ⌜n0⌝ , # σ < ⌜n0⌝ + ⌜m⌝

User applied rule constructor cut

And obtained the following new goals

Proof step 54:
σ0 = ⌜x0⌝ , ⌜x⌝ = (σ to n0 + m) + σ0 ⊦ ⌜n0⌝ + # σ0 = ⌜0⌝ , ⌜((⌜n0⌝ + ⌜m⌝ ) + # σ0).n - m⌝ = #((σ to m + n0) from m) + # σ0, # σ < ⌜m⌝ + ⌜n0⌝ , # σ < ⌜n0⌝ + ⌜m⌝

Rule argument

var: σ0

Additional information

Used simplifier rules: neq-fin-inf-01: ⊦ ⌜x⌝ ≠ σ + ⌜nf0⌝ ;%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%stream freely generated by ⌜ ⌝, ⌜ ⌝;;