Nuprl Lemma : equal_wf
∀[A:Type]. ∀[a,b:A]. (a = b ∈ A ∈ ℙ)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q
Lemmas referenced :
respects-equality-trivial,
equal-wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
hypothesisEquality,
Error :isect_memberEquality_alt,
isectElimination,
thin,
Error :isectIsTypeImplies,
Error :universeIsType,
universeEquality,
independent_functionElimination,
extract_by_obid
Latex:
\mforall{}[A:Type]. \mforall{}[a,b:A]. (a = b \mmember{} \mBbbP{})
Date html generated:
2019_06_20-AM-11_13_48
Last ObjectModification:
2018_11_21-PM-10_58_33
Theory : core_2
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