Nuprl Lemma : rel_star_trans
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. ∀x,y,z:T. ((x R y) ⇒ (y (R^*) z) ⇒ (x (R^*) z))
Proof
Definitions occuring in Statement :
rel_star: R^*,
uall: ∀[x:A]. B[x],
prop: ℙ,
infix_ap: x f y,
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
infix_ap: x f y
Lemmas referenced :
rel_star_transitivity,
rel_rel_star,
rel_star_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesisEquality,
independent_functionElimination,
dependent_functionElimination,
hypothesis,
applyEquality,
Error :functionIsType,
Error :universeIsType,
Error :inhabitedIsType,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. \mforall{}x,y,z:T. ((x R y) {}\mRightarrow{} (y rel\_star(T; R) z) {}\mRightarrow{} (x rel\_star(T; R) z))
Date html generated:
2019_06_20-PM-00_30_52
Last ObjectModification:
2018_09_26-PM-00_43_06
Theory : relations
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