Nuprl Lemma : int-product-disjoint
∀[T,S:Type]. (¬ℤ ⋂ T × S)
Proof
Definitions occuring in Statement :
isect2: T1 ⋂ T2,
uall: ∀[x:A]. B[x],
not: ¬A,
product: x:A × B[x],
int: ℤ,
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,
uimplies: b supposing a,
guard: {T},
or: P ∨ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
top: Top,
all: ∀x:A. B[x],
bfalse: ff,
sq_type: SQType(T)
Lemmas referenced :
isect2_decomp,
pair-eta,
isect2_subtype_rel3,
top_wf,
subtype_rel_product,
subtype_rel_wf,
isint-int,
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,
intEquality,
productEquality,
hypothesisEquality,
productElimination,
equalityTransitivity,
hypothesis,
equalitySymmetry,
independent_pairFormation,
applyEquality,
because_Cache,
independent_isectElimination,
sqequalRule,
inrFormation,
lambdaEquality,
isect_memberEquality,
voidElimination,
voidEquality,
instantiate,
dependent_functionElimination,
independent_functionElimination,
universeEquality
Latex:
\mforall{}[T,S:Type]. (\mneg{}\mBbbZ{} \mcap{} T \mtimes{} S)
Date html generated:
2016_05_15-PM-10_07_59
Last ObjectModification:
2015_12_27-PM-06_01_04
Theory : eval!all
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