Nuprl Lemma : sq_stable__t-sqle
∀[T:Type]. ∀[a,b:T].  SqStable(t-sqle(T;a;b))
Proof
Definitions occuring in Statement : 
t-sqle: t-sqle(T;a;b)
, 
sq_stable: SqStable(P)
, 
uall: ∀[x:A]. B[x]
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
t-sqle: t-sqle(T;a;b)
, 
subtype_rel: A ⊆r B
, 
so_lambda: λ2x.t[x]
, 
per-class: per-class(T;a)
, 
so_apply: x[s]
, 
sq_stable: SqStable(P)
, 
implies: P 
⇒ Q
, 
squash: ↓T
, 
prop: ℙ
Lemmas referenced : 
t-sqle_wf, 
squash_wf, 
sqle_wf_base, 
base_wf, 
subtype_rel_b-union-right, 
per-class_wf, 
exists_wf, 
sq_stable__squash
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
cumulativity, 
hypothesisEquality, 
applyEquality, 
hypothesis, 
because_Cache, 
sqequalRule, 
lambdaEquality, 
setElimination, 
rename, 
dependent_functionElimination, 
imageElimination, 
imageMemberEquality, 
baseClosed, 
isect_memberEquality, 
universeEquality
Latex:
\mforall{}[T:Type].  \mforall{}[a,b:T].    SqStable(t-sqle(T;a;b))
Date html generated:
2016_05_13-PM-04_12_48
Last ObjectModification:
2016_01_14-PM-07_29_24
Theory : subtype_1
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