Nuprl Lemma : sq_stable__uiff
∀[P,Q:ℙ].  (SqStable(P) 
⇒ SqStable(Q) 
⇒ SqStable(uiff(P;Q)))
Proof
Definitions occuring in Statement : 
sq_stable: SqStable(P)
, 
uiff: uiff(P;Q)
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
implies: P 
⇒ Q
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
implies: P 
⇒ Q
, 
member: t ∈ T
, 
prop: ℙ
, 
uimplies: b supposing a
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
Lemmas referenced : 
sq_stable_wf, 
sq_stable__and, 
isect_wf, 
sq_stable__uimplies
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
Error :isect_memberFormation_alt, 
lambdaFormation, 
cut, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
Error :inhabitedIsType, 
Error :universeIsType, 
universeEquality, 
cumulativity, 
sqequalRule, 
lambdaEquality, 
isect_memberEquality, 
independent_functionElimination, 
because_Cache
Latex:
\mforall{}[P,Q:\mBbbP{}].    (SqStable(P)  {}\mRightarrow{}  SqStable(Q)  {}\mRightarrow{}  SqStable(uiff(P;Q)))
Date html generated:
2019_06_20-AM-11_15_21
Last ObjectModification:
2018_09_26-AM-09_59_32
Theory : core_2
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