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Proof step 11 from proof swap-to-from-app (previous step)

#((σ to n0 + m) + σ0 from m) = #((σ to m + n0) from m) + # σ0 ⊦ # σ < ⌜n0⌝ + ⌜m⌝ , # σ < ⌜m⌝ + ⌜n0⌝ , #((σ to n0 + m) + σ0 from m) = #((σ to m + n0) from m) + # σ0 ∧ (⌜n⌝ < #((σ to n0 + m) + σ0 from m) → ((σ to n0 + m) + σ0 from m)[n] = (((σ to m + n0) from m) + σ0)[n])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
#((σ to n0 + m) + σ0 from m) = #((σ to m + n0) from m) + # σ0, ⌜n⌝ < #((σ to m + n0) from m) + # σ0 ⊦ ((σ to n0 + m) + σ0 from m)[n] = (((σ to m + n0) from m) + σ0)[n], # σ < ⌜n0⌝ + ⌜m⌝ , # σ < ⌜m⌝ + ⌜n0⌝

Proof step 11 from proof swap-to-from-app (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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