Nuprl Lemma : sq_stable__sublist-rec
∀[T:Type]. ∀l1,l2:T List. ((∀x,y:T. Dec(x = y ∈ T)) ⇒ SqStable(sublist-rec(T;l1;l2)))
Proof
Definitions occuring in Statement :
sublist-rec: sublist-rec(T;l1;l2),
list: T List,
sq_stable: SqStable(P),
decidable: Dec(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
sq_stable_from_decidable,
sublist-rec_wf,
decidable__sublist-rec,
all_wf,
decidable_wf,
equal_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_functionElimination,
dependent_functionElimination,
because_Cache,
sqequalRule,
lambdaEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}l1,l2:T List. ((\mforall{}x,y:T. Dec(x = y)) {}\mRightarrow{} SqStable(sublist-rec(T;l1;l2)))
Date html generated:
2016_05_15-PM-03_34_10
Last ObjectModification:
2015_12_27-PM-01_12_58
Theory : general
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