Nuprl Lemma : l_all_nil_iff
∀[P:Top]. uiff((∀x∈[].P[x]);True)
Proof
Definitions occuring in Statement :
l_all: (∀x∈L.P[x]),
nil: [],
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
true: True
Definitions unfolded in proof :
l_all: (∀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],
uiff: uiff(P;Q),
and: P ∧ Q,
true: True,
prop: ℙ,
so_lambda: λ2x.t[x],
int_seg: {i..j-},
false: False,
lelt: i ≤ j < k,
guard: {T},
implies: P ⇒ Q,
so_apply: x[s]
Lemmas referenced :
top_wf,
true_wf,
less_than_irreflexivity,
less_than_transitivity1,
int_seg_wf,
all_wf,
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,
introduction,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
lambdaEquality,
setElimination,
rename,
productElimination,
hypothesisEquality,
independent_functionElimination
Latex:
\mforall{}[P:Top]. uiff((\mforall{}x\mmember{}[].P[x]);True)
Date html generated:
2016_05_14-AM-06_40_05
Last ObjectModification:
2016_01_14-PM-08_20_45
Theory : list_0
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