Nuprl Lemma : rel_plus_trans
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. Trans(T;x,y.x R+ y)
Proof
Definitions occuring in Statement :
rel_plus: R+,
trans: Trans(T;x,y.E[x; y]),
uall: ∀[x:A]. B[x],
prop: ℙ,
infix_ap: x f y,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
trans: Trans(T;x,y.E[x; y]),
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
infix_ap: x f y,
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
rel_plus_transitivity,
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,
hypothesisEquality,
independent_functionElimination,
hypothesis,
Error :universeIsType,
applyEquality,
functionExtensionality,
sqequalRule,
instantiate,
functionEquality,
cumulativity,
universeEquality,
because_Cache,
Error :functionIsType
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. Trans(T;x,y.x R\msupplus{} y)
Date html generated:
2019_06_20-PM-02_01_47
Last ObjectModification:
2019_02_26-AM-11_36_19
Theory : relations2
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