Nuprl Lemma : decidable_decision
∀[P:ℙ]. ∀[x:Dec(P)]. (x ∈ Decision)
Proof
Definitions occuring in Statement :
decision: Decision,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
decision: Decision,
decidable: Dec(P),
or: P ∨ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
prop: ℙ,
uimplies: b supposing a,
top: Top
Lemmas referenced :
subtype_rel_union,
not_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalRule,
isect_memberFormation,
introduction,
cut,
hypothesisEquality,
applyEquality,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesis,
because_Cache,
independent_isectElimination,
lambdaEquality,
isect_memberEquality,
voidElimination,
voidEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
unionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[P:\mBbbP{}]. \mforall{}[x:Dec(P)]. (x \mmember{} Decision)
Date html generated:
2019_10_15-AM-10_46_56
Last ObjectModification:
2018_09_17-PM-06_45_37
Theory : basic
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