Nuprl Lemma : oob-subtype
∀[A1,B1,A2,B2:Type]. (one_or_both(A1;B1) ⊆r one_or_both(A2;B2)) supposing ((A1 ⊆r A2) and (B1 ⊆r B2))
Proof
Definitions occuring in Statement :
one_or_both: one_or_both(A;B),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
one_or_both: one_or_both(A;B),
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_union,
subtype_rel_product,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
productEquality,
hypothesisEquality,
unionEquality,
independent_isectElimination,
lambdaEquality,
hypothesis,
lambdaFormation,
because_Cache,
axiomEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[A1,B1,A2,B2:Type].
(one\_or\_both(A1;B1) \msubseteq{}r one\_or\_both(A2;B2)) supposing ((A1 \msubseteq{}r A2) and (B1 \msubseteq{}r B2))
Date html generated:
2016_05_15-PM-05_31_12
Last ObjectModification:
2015_12_27-PM-02_10_19
Theory : general
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