Nuprl Lemma : ext-eq_weakening
∀[A,B:Type]. A ≡ B supposing A = B ∈ Type
Proof
Definitions occuring in Statement :
ext-eq: A ≡ B,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lambdaEquality,
hyp_replacement,
hypothesisEquality,
hypothesis,
equalitySymmetry,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
axiomEquality,
instantiate,
lemma_by_obid,
isectElimination,
universeEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity
Latex:
\mforall{}[A,B:Type]. A \mequiv{} B supposing A = B
Date html generated:
2016_05_13-PM-03_19_05
Last ObjectModification:
2015_12_26-AM-09_07_55
Theory : subtype_0
Home
Index