Nuprl Lemma : isect2_decomp
∀[t1,t2:Type]. ∀[x:t1 ⋂ t2]. ((x ∈ t1) ∧ (x ∈ t2))
Proof
Definitions occuring in Statement :
isect2: T1 ⋂ T2,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
cand: A c∧ B,
isect2: T1 ⋂ T2,
btrue: tt,
ifthenelse: if b then t else f fi ,
guard: {T},
subtype_rel: A ⊆r B,
bfalse: ff
Lemmas referenced :
isect2_wf,
subtype_rel_self,
btrue_wf,
bfalse_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
independent_pairFormation,
hypothesis,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :universeIsType,
extract_by_obid,
isectElimination,
hypothesisEquality,
isect_memberEquality,
because_Cache,
Error :inhabitedIsType,
universeEquality,
applyEquality
Latex:
\mforall{}[t1,t2:Type]. \mforall{}[x:t1 \mcap{} t2]. ((x \mmember{} t1) \mwedge{} (x \mmember{} t2))
Date html generated:
2019_06_20-AM-11_32_09
Last ObjectModification:
2018_09_26-AM-11_28_14
Theory : bool_1
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