Nuprl Lemma : l_all_wf_nil
∀[P:Void ⟶ Void]. ((∀x∈[].P[x]) ∈ ℙ)
Proof
Definitions occuring in Statement :
l_all: (∀x∈L.P[x]),
nil: [],
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
void: Void
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],
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
int_seg: {i..j-},
false: False,
lelt: i ≤ j < k,
and: P ∧ Q,
implies: P ⇒ Q,
subtype_rel: A ⊆r B
Lemmas referenced :
less_than_irreflexivity,
less_than_transitivity1,
void_wf,
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,
introduction,
natural_numberEquality,
because_Cache,
lambdaEquality,
applyEquality,
functionExtensionality,
hypothesisEquality,
instantiate,
setElimination,
rename,
productElimination,
independent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality
Latex:
\mforall{}[P:Void {}\mrightarrow{} Void]. ((\mforall{}x\mmember{}[].P[x]) \mmember{} \mBbbP{})
Date html generated:
2016_05_14-AM-06_40_43
Last ObjectModification:
2016_01_14-PM-08_19_42
Theory : list_0
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