Nuprl Lemma : ancestral-logic-induction
(∀x,y:Dom. ((R x y) ⇒ (B x) ⇒ (B y))) ⇒ (∀x,y:Dom. (TC(λa,b.R a b)(x,y) ⇒ (B x) ⇒ (B 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 :
language1: language1{i:l}(D,A,B,C,P,Q,R,H.fml[D;A;B;C;P;Q;R;H]),
uall: ∀[x:A]. B[x],
!hyp_hide: x,
member: t ∈ T,
prop: ℙ,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y]
Lemmas referenced :
all_wf,
TC-min-uniform
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
sqequalHypSubstitution,
functionEquality,
cumulativity,
hypothesisEquality,
universeEquality,
because_Cache,
lambdaFormation,
cut,
lemma_by_obid,
isectElimination,
thin,
sqequalRule,
lambdaEquality,
applyEquality,
hypothesis,
independent_functionElimination,
addLevel,
levelHypothesis
Latex:
(\mforall{}x,y:Dom. ((R x y) {}\mRightarrow{} (B x) {}\mRightarrow{} (B y))) {}\mRightarrow{} (\mforall{}x,y:Dom. (TC(\mlambda{}a,b.R a b)(x,y) {}\mRightarrow{} (B x) {}\mRightarrow{} (B y)))
Date html generated:
2016_05_16-AM-09_08_21
Last ObjectModification:
2015_12_28-PM-07_03_13
Theory : first-order!and!ancestral!logic
Home
Index