"All treaties with the Lakota nation are to be honoured. Thus, whatever is not to be honoured is not a treaty with the Lakota nation, and everything is either not a treaty with the Lakota nation or it is to be honoured."
The simplest form of the proof requires no more than working with the definitions as the conclusion is merely a restatement of the premise. Contraposition and material implication have been used.
- (x)(Txl ⊃Hx)
- ∴ (x)(¬ Hx ⊃¬ Txl) • (x)(¬ Txl ∨Hx)
- (x)(¬ Hx ⊃¬ Txl) ......... 1 Contrap.
- (x)(¬ Txl ∨Hx) ......... 1 MI
- (x)(¬ Hx ⊃¬ Txl) • (x)(¬ Txl ∨Hx) ......... 3,4 Conj.
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