Nuprl Lemma : decidable__implies
∀[P:ℙ]. ∀[Q:⋂p:P. 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,
isect: ⋂x:A. B[x]
Definitions unfolded in proof :
decidable: Dec(P),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
member: t ∈ T,
prop: ℙ,
subtype_rel: A ⊆r B,
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,
hypothesisEquality,
cut,
introduction,
extract_by_obid,
isectElimination,
functionEquality,
applyEquality,
lambdaEquality,
rename,
equalityTransitivity,
equalitySymmetry,
isectEquality,
cumulativity,
universeEquality,
inrFormation,
voidElimination,
because_Cache,
Error :isectIsType,
Error :universeIsType,
Error :inhabitedIsType
Latex:
\mforall{}[P:\mBbbP{}]. \mforall{}[Q:\mcap{}p:P. \mBbbP{}]. (Dec(P) {}\mRightarrow{} (P {}\mRightarrow{} Dec(Q)) {}\mRightarrow{} Dec(P {}\mRightarrow{} Q))
Date html generated:
2019_06_20-AM-11_14_58
Last ObjectModification:
2018_09_26-AM-10_42_05
Theory : core_2
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