Nuprl Lemma : decidable__and
∀[P,Q:ℙ]. (Dec(P) ⇒ (P ⇒ Dec(Q)) ⇒ Dec(P ∧ Q))
Proof
Definitions occuring in Statement :
decidable: Dec(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q,
and: P ∧ Q
Definitions unfolded in proof :
decidable: Dec(P),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
and: P ∧ Q,
cand: A c∧ B,
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,
independent_functionElimination,
hypothesis,
inlFormation,
cut,
independent_pairFormation,
introduction,
extract_by_obid,
isectElimination,
productEquality,
cumulativity,
hypothesisEquality,
inrFormation,
productElimination,
voidElimination,
functionEquality,
Error :inhabitedIsType,
Error :universeIsType,
universeEquality
Latex:
\mforall{}[P,Q:\mBbbP{}]. (Dec(P) {}\mRightarrow{} (P {}\mRightarrow{} Dec(Q)) {}\mRightarrow{} Dec(P \mwedge{} Q))
Date html generated:
2019_06_20-AM-11_14_56
Last ObjectModification:
2018_09_26-AM-10_42_08
Theory : core_2
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