Nuprl Lemma : ext-eq_wf
∀[A,B:Type]. (A ≡ B ∈ ℙ)
Proof
Definitions occuring in Statement :
ext-eq: A ≡ B,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
ext-eq: A ≡ B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ
Lemmas referenced :
and_wf,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[A,B:Type]. (A \mequiv{} B \mmember{} \mBbbP{})
Date html generated:
2016_05_13-PM-03_19_04
Last ObjectModification:
2015_12_26-AM-09_07_57
Theory : subtype_0
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