Nuprl Lemma : ancestral-logic-example1
(∀x,y:Dom. ((P x y) ⇒ (Q x y))) ⇒ (∀x,y:Dom. (TC(λa,b.P a b)(x,y) ⇒ TC(λa,b.Q a b)(x,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],
implies: P ⇒ Q,
apply: f a
Lemmas :
all_wf,
TC-base,
TC-min-uniform,
TC_wf,
TC-trans
(\mforall{}x,y:Dom. ((P x y) {}\mRightarrow{} (Q x y))) {}\mRightarrow{} (\mforall{}x,y:Dom. (TC(\mlambda{}a,b.P a b)(x,y) {}\mRightarrow{} TC(\mlambda{}a,b.Q a b)(x,y)))
Date html generated:
2015_07_17-AM-07_53_00
Last ObjectModification:
2015_01_30-AM-09_47_13
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