Nuprl Lemma : rel-diamond-property_wf
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. (rel-diamond-property(T;x,y.R[x;y]) ∈ ℙ)
Proof
Definitions occuring in Statement :
rel-diamond-property: rel-diamond-property(T;x,y.R[x; y]),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rel-diamond-property: rel-diamond-property(T;x,y.R[x; y]),
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_apply: x[s1;s2],
or: P ∨ Q,
exists: ∃x:A. B[x],
and: P ∧ Q,
subtype_rel: A ⊆r B
Lemmas referenced :
equal_wf,
subtype_rel_self,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
functionEquality,
hypothesisEquality,
applyEquality,
unionEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
productEquality,
instantiate,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionIsType,
universeIsType,
universeEquality,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. (rel-diamond-property(T;x,y.R[x;y]) \mmember{} \mBbbP{})
Date html generated:
2019_10_15-AM-10_24_32
Last ObjectModification:
2019_08_16-PM-02_28_59
Theory : relations2
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