Nuprl Lemma : rel_or_wf
∀[T:Type]. ∀[R1,R2:T ⟶ T ⟶ ℙ]. (R1 ∨ R2 ∈ T ⟶ T ⟶ ℙ)
Proof
Definitions occuring in Statement :
rel_or: R1 ∨ 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_or: R1 ∨ R2,
infix_ap: x f y,
prop: ℙ
Lemmas referenced :
or_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
lambdaEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
isect_memberEquality,
functionEquality,
cumulativity,
universeEquality,
Error :functionIsType,
Error :universeIsType,
because_Cache
Latex:
\mforall{}[T:Type]. \mforall{}[R1,R2:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. (R1 \mvee{} R2 \mmember{} T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{})
Date html generated:
2019_06_20-PM-00_31_05
Last ObjectModification:
2018_09_26-PM-00_39_31
Theory : relations
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