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Decomposition of Disjunctions

Proposition: For proving with knowledge K the goal G₀ \/ G₁, it suffices to prove G₁ with additional knowledge ~G₀:

K

G0 \/ G1

~~>

K union {~G0}

G1

"We have to show G₀ \/ G₁. Assume ~G₀. Then ...(proof of G₁)."

• Consequence of "(G₀ \/ G₁) iff (~G₀ => G₁)".
• Roles of G₀ and G₁ can be inverted.

Same techniques as for decomposition of implications.