Nuprl Lemma : ancestral-logic-example1-ext
(∀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
Definitions unfolded in proof :
member: t ∈ T,
ancestral-logic-example1,
TC-min-uniform,
transitive-closure-minimal-uniform,
spreadn: spread3,
TC-trans,
transitive-closure-transitive,
TC-base,
transitive-closure-contains,
cons: [a / b],
nil: [],
it: ⋅
Lemmas referenced :
ancestral-logic-example1,
TC-min-uniform,
transitive-closure-minimal-uniform,
TC-trans,
transitive-closure-transitive,
TC-base,
transitive-closure-contains
Rules used in proof :
introduction,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
instantiate,
extract_by_obid,
hypothesis,
sqequalRule,
thin,
sqequalHypSubstitution,
equalityTransitivity,
equalitySymmetry
Latex:
(\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:
2016_05_16-AM-09_08_29
Last ObjectModification:
2015_12_28-PM-07_03_12
Theory : first-order!and!ancestral!logic
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