Nuprl Lemma : subtype_rel_functionality_wrt_implies
∀[A,B,C,D:Type]. ({C ⊆r D supposing A ⊆r B}) supposing ((B ⊆r D) and (A ⊇r C))
Proof
Definitions occuring in Statement :
rev_subtype_rel: A ⊇r B,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
guard: {T},
universe: Type
Definitions unfolded in proof :
guard: {T},
rev_subtype_rel: A ⊇r B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B
Lemmas referenced :
subtype_rel_transitivity,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
axiomEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[A,B,C,D:Type]. (\{C \msubseteq{}r D supposing A \msubseteq{}r B\}) supposing ((B \msubseteq{}r D) and (A \msupseteq{}r C))
Date html generated:
2016_05_13-PM-03_19_10
Last ObjectModification:
2015_12_26-AM-09_07_51
Theory : subtype_0
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