Nuprl Lemma : not_over_and
∀[A,B:ℙ]. (Dec(A) ⇒ (¬(A ∧ B) ⇐⇒ (¬A) ∨ (¬B)))
Proof
Definitions occuring in Statement :
decidable: Dec(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
iff: P ⇐⇒ Q,
not: ¬A,
implies: P ⇒ Q,
or: P ∨ Q,
and: P ∧ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
guard: {T},
not: ¬A,
false: False,
cand: A c∧ B,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q,
uimplies: b supposing a
Lemmas referenced :
not_wf,
or_wf,
decidable_wf,
not_over_and_b
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
lambdaFormation,
independent_pairFormation,
cut,
hypothesis,
sqequalHypSubstitution,
unionElimination,
thin,
sqequalRule,
inrFormation,
independent_functionElimination,
hypothesisEquality,
introduction,
extract_by_obid,
isectElimination,
inlFormation,
productEquality,
cumulativity,
voidElimination,
Error :inhabitedIsType,
Error :universeIsType,
universeEquality,
independent_isectElimination
Latex:
\mforall{}[A,B:\mBbbP{}]. (Dec(A) {}\mRightarrow{} (\mneg{}(A \mwedge{} B) \mLeftarrow{}{}\mRightarrow{} (\mneg{}A) \mvee{} (\mneg{}B)))
Date html generated:
2019_06_20-AM-11_16_09
Last ObjectModification:
2018_09_26-AM-10_24_00
Theory : core_2
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