Nuprl Lemma : equal-wf-T-base
∀[T:Type]. ∀[a:T]. ∀[b:Base]. (a = b ∈ T ∈ ℙ)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
base: Base,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
guard: {T},
implies: P ⇒ Q
Lemmas referenced :
istype-base,
base_wf,
base-respects-equality,
respects-equality-trivial,
equal-wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
hypothesis,
Error :universeIsType,
hypothesisEquality,
universeEquality,
sqequalHypSubstitution,
isectElimination,
thin,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[a:T]. \mforall{}[b:Base]. (a = b \mmember{} \mBbbP{})
Date html generated:
2019_06_20-AM-11_13_48
Last ObjectModification:
2018_11_25-PM-06_17_12
Theory : core_2
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