Nuprl Lemma : subtype_rel_weakening
∀[A,B:Type]. A ⊆r B supposing A ≡ B
Proof
Definitions occuring in Statement :
ext-eq: A ≡ B,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
ext-eq: A ≡ B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
and: P ∧ Q,
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
and_wf,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
hypothesis,
axiomEquality,
lemma_by_obid,
isectElimination,
hypothesisEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[A,B:Type]. A \msubseteq{}r B supposing A \mequiv{} B
Date html generated:
2016_05_13-PM-03_19_11
Last ObjectModification:
2015_12_26-AM-09_07_50
Theory : subtype_0
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