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
Home
Index