Nuprl Lemma : rel-comp_wf
∀[A,B,C:Type]. ∀[R1:A ⟶ B ⟶ ℙ]. ∀[R2:B ⟶ C ⟶ ℙ]. ((R1 o R2) ∈ A ⟶ C ⟶ ℙ)
Proof
Definitions occuring in Statement :
rel-comp: (R1 o R2),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rel-comp: (R1 o R2),
prop: ℙ,
exists: ∃x:A. B[x],
and: P ∧ Q,
subtype_rel: A ⊆r B
Lemmas referenced :
subtype_rel_self,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
Error :lambdaEquality_alt,
productEquality,
hypothesisEquality,
applyEquality,
hypothesis,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
because_Cache,
Error :universeIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :functionIsType,
universeEquality,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies,
Error :inhabitedIsType
Latex:
\mforall{}[A,B,C:Type]. \mforall{}[R1:A {}\mrightarrow{} B {}\mrightarrow{} \mBbbP{}]. \mforall{}[R2:B {}\mrightarrow{} C {}\mrightarrow{} \mBbbP{}]. ((R1 o R2) \mmember{} A {}\mrightarrow{} C {}\mrightarrow{} \mBbbP{})
Date html generated:
2019_06_20-PM-00_31_19
Last ObjectModification:
2019_03_27-PM-00_41_31
Theory : relations
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