Nuprl Lemma : subtype_rel_simple_product
∀[A,B,C,D:Type]. ((A × B) ⊆r (C × D)) supposing ((B ⊆r D) and (A ⊆r C))
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
subtype_rel: A ⊆r B
Lemmas referenced :
subtype_rel_product,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
lambdaEquality,
independent_isectElimination,
hypothesis,
lambdaFormation,
because_Cache,
axiomEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[A,B,C,D:Type]. ((A \mtimes{} B) \msubseteq{}r (C \mtimes{} D)) supposing ((B \msubseteq{}r D) and (A \msubseteq{}r C))
Date html generated:
2016_05_13-PM-03_18_41
Last ObjectModification:
2015_12_26-AM-09_08_21
Theory : subtype_0
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