Nuprl Lemma : subtype_rel_tagged+
∀[T1,T2,B1,B2:Type]. (∀[z:Atom]. (T1 |+ z:B1 ⊆r T2 |+ z:B2)) supposing ((B1 ⊆r B2) and (T1 ⊆r T2))
Proof
Definitions occuring in Statement :
tagged+: T |+ z:B,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
atom: Atom,
universe: Type
Definitions unfolded in proof :
tagged+: T |+ z:B,
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,
or: P ∨ Q
Lemmas referenced :
isect2_subtype_rel,
tag-case_wf,
subtype_rel_transitivity,
isect2_wf,
isect2_subtype_rel3,
subtype_rel-tag-case,
subtype_rel_wf,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
isect_memberEquality,
sqequalHypSubstitution,
unionElimination,
thin,
equalityElimination,
hypothesisEquality,
applyEquality,
lemma_by_obid,
isectElimination,
hypothesis,
because_Cache,
independent_isectElimination,
inrFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[T1,T2,B1,B2:Type]. (\mforall{}[z:Atom]. (T1 |+ z:B1 \msubseteq{}r T2 |+ z:B2)) supposing ((B1 \msubseteq{}r B2) and (T1 \msubseteq{}r T2))
Date html generated:
2016_05_15-PM-06_46_44
Last ObjectModification:
2015_12_27-AM-11_50_23
Theory : general
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