Assume Heq: Zplus = R.

We will prove False.

We prove the intermediate claim H0R: 0 ∈ R.

An exact proof term for the current goal is real_0.

We prove the intermediate claim H0Z: 0 ∈ Zplus.

rewrite the current goal using Heq (from left to right).

An exact proof term for the current goal is H0R.

An exact proof term for the current goal is (zero_not_in_Zplus H0Z).

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