Nuprl Lemma : iff_preserves_decidability
∀[A,B:ℙ].  (Dec(A) 
⇒ (A 
⇐⇒ B) 
⇒ Dec(B))
Proof
Definitions occuring in Statement : 
decidable: Dec(P)
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
iff: P 
⇐⇒ Q
, 
implies: P 
⇒ Q
Definitions unfolded in proof : 
decidable: Dec(P)
, 
uall: ∀[x:A]. B[x]
, 
implies: P 
⇒ Q
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
or: P ∨ Q
, 
member: t ∈ T
, 
prop: ℙ
, 
guard: {T}
, 
not: ¬A
, 
false: False
, 
rev_implies: P 
⇐ Q
Lemmas referenced : 
not_wf, 
iff_wf, 
or_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
Error :isect_memberFormation_alt, 
lambdaFormation, 
sqequalHypSubstitution, 
productElimination, 
thin, 
unionElimination, 
independent_functionElimination, 
hypothesis, 
inlFormation, 
cut, 
introduction, 
extract_by_obid, 
isectElimination, 
hypothesisEquality, 
inrFormation, 
Error :inhabitedIsType, 
Error :universeIsType, 
universeEquality, 
voidElimination
Latex:
\mforall{}[A,B:\mBbbP{}].    (Dec(A)  {}\mRightarrow{}  (A  \mLeftarrow{}{}\mRightarrow{}  B)  {}\mRightarrow{}  Dec(B))
Date html generated:
2019_06_20-AM-11_15_06
Last ObjectModification:
2018_09_26-AM-10_42_12
Theory : core_2
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