Nuprl Lemma : ancestral-logic-lemma1
∀x,y:Dom. (TC(λa,b.R a b)(x,y) ⇒ ((R x y) ∨ (∃z:Dom. ((R x z) ∧ TC(λa,b.R a b)(z,y)))))
Proof
Definitions occuring in Statement :
TC: TC(λx,y.F[x; y])(a,b),
language1: language1{i:l}(D,A,B,C,P,Q,R,H.fml[D;A;B;C;P;Q;R;H]),
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
and: P ∧ Q,
apply: f a
Lemmas :
exists_wf,
TC_wf,
TC-min,
or_wf,
TC-base,
TC-trans
\mforall{}x,y:Dom. (TC(\mlambda{}a,b.R a b)(x,y) {}\mRightarrow{} ((R x y) \mvee{} (\mexists{}z:Dom. ((R x z) \mwedge{} TC(\mlambda{}a,b.R a b)(z,y)))))
Date html generated:
2015_07_17-AM-07_52_54
Last ObjectModification:
2015_01_30-AM-09_47_20
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