Nuprl Lemma : sorted_wf
∀[T:Type]. ∀[L:T List]. (sorted(L) ∈ ℙ) supposing T ⊆r ℤ
Proof
Definitions occuring in Statement :
sorted: sorted(L),
list: T List,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
int: ℤ,
universe: Type
Definitions unfolded in proof :
sorted: sorted(L),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
int_seg: {i..j-},
sq_stable: SqStable(P),
implies: P ⇒ Q,
lelt: i ≤ j < k,
and: P ∧ Q,
squash: ↓T,
guard: {T},
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
so_apply: x[s]
Lemmas referenced :
subtype_rel_wf,
list_wf,
le_weakening2,
less_than_transitivity2,
sq_stable__le,
select_wf,
le_wf,
length_wf,
int_seg_wf,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
cumulativity,
hypothesisEquality,
hypothesis,
lambdaEquality,
because_Cache,
setElimination,
rename,
independent_isectElimination,
independent_functionElimination,
productElimination,
imageMemberEquality,
baseClosed,
imageElimination,
dependent_functionElimination,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
intEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. (sorted(L) \mmember{} \mBbbP{}) supposing T \msubseteq{}r \mBbbZ{}
Date html generated:
2016_05_14-AM-06_36_10
Last ObjectModification:
2016_01_14-PM-08_22_31
Theory : list_0
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