Nuprl Lemma : prop_and_wf
∀[T:Type]. ∀[P,Q:T ⟶ ℙ]. (P ∧ Q ∈ T ⟶ ℙ)
Proof
Definitions occuring in Statement :
prop_and: P ∧ Q,
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,
prop_and: P ∧ Q,
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B
Lemmas referenced :
subtype_rel_self
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
lambdaEquality,
productEquality,
applyEquality,
hypothesisEquality,
hypothesis,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
universeEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
isect_memberEquality,
functionEquality,
cumulativity,
Error :functionIsType,
Error :universeIsType
Latex:
\mforall{}[T:Type]. \mforall{}[P,Q:T {}\mrightarrow{} \mBbbP{}]. (P \mwedge{} Q \mmember{} T {}\mrightarrow{} \mBbbP{})
Date html generated:
2019_06_20-PM-00_31_39
Last ObjectModification:
2018_09_26-AM-11_46_31
Theory : relations
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