Nuprl Lemma : union-product-disjoint
∀[T,S,A,B:Type]. (¬A + B ⋂ T × S)
Proof
Definitions occuring in Statement :
isect2: T1 ⋂ T2,
uall: ∀[x:A]. B[x],
not: ¬A,
product: x:A × B[x],
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
and: P ∧ Q,
cand: A c∧ B,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
prop: ℙ
Lemmas referenced :
isect2_wf,
btrue_neq_bfalse,
isect2_decomp,
isect2_subtype_rel2,
equal_wf,
btrue_wf,
isect2_subtype_rel,
bfalse_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
hypothesis,
sqequalHypSubstitution,
independent_functionElimination,
voidElimination,
extract_by_obid,
isectElimination,
unionEquality,
cumulativity,
hypothesisEquality,
productEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
because_Cache,
universeEquality,
isect_memberEquality,
rename,
independent_pairFormation,
productElimination,
equalityTransitivity,
equalitySymmetry,
applyEquality,
unionElimination
Latex:
\mforall{}[T,S,A,B:Type]. (\mneg{}A + B \mcap{} T \mtimes{} S)
Date html generated:
2018_05_21-PM-10_19_09
Last ObjectModification:
2017_07_26-PM-06_36_51
Theory : eval!all
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