Nuprl Lemma : atom-product-disjoint
∀[T,S:Type]. (¬Atom ⋂ T × S)
Proof
Definitions occuring in Statement :
isect2: T1 ⋂ T2,
uall: ∀[x:A]. B[x],
not: ¬A,
product: x:A × B[x],
atom: Atom,
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,
uimplies: b supposing a,
bfalse: ff,
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T}
Lemmas referenced :
isect2_decomp,
pair-eta,
subtype_base_sq,
bool_subtype_base,
bfalse_wf,
btrue_neq_bfalse,
isect2_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
rename,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
atomEquality,
productEquality,
hypothesisEquality,
productElimination,
equalityTransitivity,
hypothesis,
equalitySymmetry,
independent_pairFormation,
isatomReduceTrue,
because_Cache,
instantiate,
independent_isectElimination,
sqequalRule,
dependent_functionElimination,
independent_functionElimination,
voidElimination,
lambdaEquality,
universeEquality,
isect_memberEquality
Latex:
\mforall{}[T,S:Type]. (\mneg{}Atom \mcap{} T \mtimes{} S)
Date html generated:
2016_05_15-PM-10_07_57
Last ObjectModification:
2015_12_27-PM-06_00_39
Theory : eval!all
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