Nuprl Lemma : and_functionality_wrt_rev_uimplies
∀[P1,P2,Q1,Q2:ℙ].  ({rev_uimplies(P1;P2)} 
⇒ {rev_uimplies(Q1;Q2)} 
⇒ {rev_uimplies(P1 ∧ Q1;P2 ∧ Q2)})
Proof
Definitions occuring in Statement : 
rev_uimplies: rev_uimplies(P;Q)
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
guard: {T}
, 
implies: P 
⇒ Q
, 
and: P ∧ Q
Definitions unfolded in proof : 
guard: {T}
, 
uall: ∀[x:A]. B[x]
, 
implies: P 
⇒ Q
, 
rev_uimplies: rev_uimplies(P;Q)
, 
uimplies: b supposing a
, 
and: P ∧ Q
, 
cand: A c∧ B
, 
prop: ℙ
, 
member: t ∈ T
Lemmas referenced : 
rev_uimplies_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
Error :isect_memberFormation_alt, 
lambdaFormation, 
cut, 
sqequalHypSubstitution, 
hypothesis, 
independent_isectElimination, 
thin, 
productElimination, 
independent_pairFormation, 
Error :productIsType, 
Error :universeIsType, 
hypothesisEquality, 
introduction, 
extract_by_obid, 
isectElimination, 
Error :inhabitedIsType, 
universeEquality
Latex:
\mforall{}[P1,P2,Q1,Q2:\mBbbP{}].
    (\{rev\_uimplies(P1;P2)\}  {}\mRightarrow{}  \{rev\_uimplies(Q1;Q2)\}  {}\mRightarrow{}  \{rev\_uimplies(P1  \mwedge{}  Q1;P2  \mwedge{}  Q2)\})
Date html generated:
2019_06_20-AM-11_14_14
Last ObjectModification:
2018_09_26-AM-10_41_50
Theory : core_2
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