Assume Heq: setprod R R = ω.

We will prove False.

We prove the intermediate claim HpRR: (0,1) ∈ setprod R R.

An exact proof term for the current goal is (tuple_2_setprod_by_pair_Sigma R R 0 1 real_0 real_1).

We prove the intermediate claim HpOmega: (0,1) ∈ ω.

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

An exact proof term for the current goal is HpRR.

We prove the intermediate claim HSingOmega: {1} ∈ ω.

rewrite the current goal using tuple_0_1_eq_Sing1 (from right to left).

An exact proof term for the current goal is HpOmega.

An exact proof term for the current goal is (Sing1_not_in_omega HSingOmega).

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