Nuprl Lemma : l_exists_nil
∀[P:Top]. ((∃x∈[]. P[x]) ⇐⇒ False)
Proof
Definitions occuring in Statement :
l_exists: (∃x∈L. P[x]),
nil: [],
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
iff: P ⇐⇒ Q,
false: False
Definitions unfolded in proof :
l_exists: (∃x∈L. P[x]),
select: L[n],
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
nil: [],
it: ⋅,
so_lambda: λ2x y.t[x; y],
top: Top,
so_apply: x[s1;s2],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
false: False,
exists: ∃x:A. B[x],
int_seg: {i..j-},
lelt: i ≤ j < k,
guard: {T},
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_implies: P ⇐ Q
Lemmas referenced :
top_wf,
false_wf,
int_seg_wf,
exists_wf,
less_than_irreflexivity,
less_than_transitivity1,
base_wf,
stuck-spread,
length_of_nil_lemma
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
lemma_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
baseClosed,
independent_isectElimination,
lambdaFormation,
isect_memberEquality,
voidElimination,
voidEquality,
isect_memberFormation,
independent_pairFormation,
productElimination,
setElimination,
rename,
hypothesisEquality,
natural_numberEquality,
independent_functionElimination,
because_Cache,
lambdaEquality
Latex:
\mforall{}[P:Top]. ((\mexists{}x\mmember{}[]. P[x]) \mLeftarrow{}{}\mRightarrow{} False)
Date html generated:
2016_05_14-AM-06_40_22
Last ObjectModification:
2016_01_06-PM-08_33_59
Theory : list_0
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