Nuprl Lemma : sq_stable__equal
∀[A:Type]. ∀[x,y:A]. SqStable(x = y ∈ A)
Proof
Definitions occuring in Statement :
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T
Lemmas referenced :
squash_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
Error :inhabitedIsType,
because_Cache,
Error :universeIsType,
universeEquality,
sqequalRule,
Error :isect_memberFormation_alt,
lambdaFormation,
lambdaEquality,
dependent_functionElimination,
axiomEquality,
isect_memberEquality,
imageElimination
Latex:
\mforall{}[A:Type]. \mforall{}[x,y:A]. SqStable(x = y)
Date html generated:
2019_06_20-AM-11_15_28
Last ObjectModification:
2018_09_26-AM-09_59_35
Theory : core_2
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