Nuprl Lemma : nequal_wf
∀[A:Type]. ∀[x,y:A]. (x ≠ y ∈ A ∈ ℙ)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
prop: ℙ,
nequal: a ≠ b ∈ T ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nequal: a ≠ b ∈ T
Lemmas referenced :
not_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
isect_memberEquality,
Error :universeIsType,
because_Cache,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[x,y:A]. (x \mneq{} y \mmember{} A \mmember{} \mBbbP{})
Date html generated:
2019_06_20-AM-11_14_34
Last ObjectModification:
2018_09_26-AM-10_41_59
Theory : core_2
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