Nuprl Lemma : rel-plus-implies-rel-star
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. ∀x,y:T. ((x R+ y) ⇒ (x (R^*) y))
Proof
Definitions occuring in Statement :
rel_plus: R+,
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,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
or: P ∨ Q,
infix_ap: x f y,
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
rel-star-iff-rel-plus-or,
rel_plus_wf,
subtype_rel_self,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
Error :lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
dependent_functionElimination,
productElimination,
independent_functionElimination,
Error :inlFormation_alt,
hypothesis,
Error :equalityIstype,
Error :inhabitedIsType,
hypothesisEquality,
Error :universeIsType,
applyEquality,
functionExtensionality,
sqequalRule,
instantiate,
functionEquality,
cumulativity,
universeEquality,
Error :functionIsType
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. \mforall{}x,y:T. ((x R\msupplus{} y) {}\mRightarrow{} (x rel\_star(T; R) y))
Date html generated:
2019_06_20-PM-02_01_52
Last ObjectModification:
2019_03_28-PM-03_10_09
Theory : relations2
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