Nuprl Lemma : decidable__or

∀[P,Q:ℙ].  (Dec(P) ⇒ Dec(Q) ⇒ Dec(P ∨ Q))


Proof




Definitions occuring in Statement :  decidable: Dec(P),  uall: ∀[x:A]. B[x],  prop: ℙ,  implies: P ⇒ Q,  or: P ∨ Q
Definitions unfolded in proof :  decidable: Dec(P),  uall: ∀[x:A]. B[x],  implies: P ⇒ Q,  or: P ∨ Q,  member: t ∈ T,  prop: ℙ,  guard: {T},  not: ¬A,  false: False
Lemmas referenced :  not_wf,  or_wf
Rules used in proof :  sqequalSubstitution,  sqequalRule,  sqequalReflexivity,  sqequalTransitivity,  computationStep,  Error :isect_memberFormation_alt,  lambdaFormation,  sqequalHypSubstitution,  unionElimination,  thin,  inlFormation,  hypothesis,  hypothesisEquality,  cut,  introduction,  extract_by_obid,  isectElimination,  inrFormation,  independent_functionElimination,  voidElimination,  because_Cache,  Error :inhabitedIsType,  Error :universeIsType,  universeEquality

Latex:
\mforall{}[P,Q:\mBbbP{}].    (Dec(P)  {}\mRightarrow{}  Dec(Q)  {}\mRightarrow{}  Dec(P  \mvee{}  Q))



Date html generated: 2019_06_20-AM-11_14_54
Last ObjectModification: 2018_09_26-AM-10_42_07

Theory : core_2


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