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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