Nuprl Lemma : union-atom-disjoint
∀[T,S:Type]. (¬T + S ⋂ Atom)
Proof
Definitions occuring in Statement :
isect2: T1 ⋂ T2,
uall: ∀[x:A]. B[x],
not: ¬A,
union: left + right,
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,
all: ∀x:A. B[x],
or: P ∨ Q,
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T},
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff
Lemmas referenced :
isect2_decomp,
injection-eta,
bool_cases,
subtype_base_sq,
bool_subtype_base,
eqtt_to_assert,
bfalse_wf,
eqff_to_assert,
assert_of_bnot,
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,
unionEquality,
hypothesisEquality,
atomEquality,
productElimination,
equalityTransitivity,
hypothesis,
equalitySymmetry,
independent_pairFormation,
isatomReduceTrue,
dependent_functionElimination,
because_Cache,
unionElimination,
instantiate,
independent_isectElimination,
independent_functionElimination,
sqequalRule,
voidElimination,
lambdaEquality,
universeEquality,
isect_memberEquality
Latex:
\mforall{}[T,S:Type]. (\mneg{}T + S \mcap{} Atom)
Date html generated:
2016_05_15-PM-10_08_05
Last ObjectModification:
2015_12_27-PM-06_00_38
Theory : eval!all
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