Nuprl Lemma : std-simplex-void
∀[n:ℤ]. ¬Δ(n) supposing n < 0
Proof
Definitions occuring in Statement :
std-simplex: Δ(n),
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
std-simplex: Δ(n),
and: P ∧ Q,
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s],
uiff: uiff(P;Q),
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T},
true: True
Lemmas referenced :
std-simplex_wf,
istype-less_than,
istype-int,
rsum-empty,
istype-void,
req-int,
subtype_base_sq,
int_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
lambdaFormation_alt,
thin,
sqequalHypSubstitution,
setElimination,
rename,
productElimination,
hypothesis,
because_Cache,
independent_functionElimination,
voidElimination,
universeIsType,
extract_by_obid,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality_alt,
dependent_functionElimination,
functionIsTypeImplies,
inhabitedIsType,
natural_numberEquality,
isect_memberEquality_alt,
isectIsTypeImplies,
independent_isectElimination,
instantiate,
cumulativity,
intEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[n:\mBbbZ{}]. \mneg{}\mDelta{}(n) supposing n < 0
Date html generated:
2019_10_30-AM-11_30_29
Last ObjectModification:
2019_07_31-PM-02_48_41
Theory : real!vectors
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