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Alternative

Because of (G₀ => G₁) iff (~G₁ => ~G₀), it suffices to prove

K

G0 => G1

~~>

K union {~G1}

~G0

"We show G₀ => G₁. Assume ~G₁. Then ...(proof of ~G₀ with additional knowledge ~G₁)."

Reverse the direction of the implication.