Nuprl Lemma : isect2_functionality_wrt_subtype_rel
∀[A1,B1,A2,B2:Type]. (A1 ⋂ B1 ⊆r A2 ⋂ B2) supposing ((A1 ⊆r A2) and (B1 ⊆r B2))
Proof
Definitions occuring in Statement :
isect2: T1 ⋂ T2,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
isect2: T1 ⋂ T2,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
guard: {T},
bfalse: ff
Lemmas referenced :
subtype_rel_wf,
isect2_subtype_rel,
subtype_rel_transitivity,
isect2_wf,
isect2_subtype_rel2,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
axiomEquality,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
lambdaEquality,
unionElimination,
equalityElimination,
applyEquality,
independent_isectElimination
Latex:
\mforall{}[A1,B1,A2,B2:Type]. (A1 \mcap{} B1 \msubseteq{}r A2 \mcap{} B2) supposing ((A1 \msubseteq{}r A2) and (B1 \msubseteq{}r B2))
Date html generated:
2016_05_13-PM-04_10_45
Last ObjectModification:
2015_12_26-AM-11_22_47
Theory : subtype_1
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