Nuprl Lemma : product-unit-disjoint
∀[T,S:Type]. (¬T × S ⋂ Unit)
Proof
Definitions occuring in Statement :
isect2: T1 ⋂ T2,
uall: ∀[x:A]. B[x],
not: ¬A,
unit: Unit,
product: x:A × B[x],
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,
unit: Unit
Lemmas referenced :
btrue_neq_bfalse,
isect2_wf,
unit_wf2,
isect2_decomp,
isect2_subtype_rel,
btrue_wf,
equal_wf,
isect2_subtype_rel2,
bfalse_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
rename,
independent_pairFormation,
hypothesis,
sqequalHypSubstitution,
productElimination,
equalityTransitivity,
equalitySymmetry,
extract_by_obid,
independent_functionElimination,
voidElimination,
because_Cache,
isectElimination,
productEquality,
cumulativity,
hypothesisEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
universeEquality,
isect_memberEquality,
applyEquality,
equalityElimination
Latex:
\mforall{}[T,S:Type]. (\mneg{}T \mtimes{} S \mcap{} Unit)
Date html generated:
2018_05_21-PM-10_19_05
Last ObjectModification:
2017_07_26-PM-06_36_50
Theory : eval!all
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