Nuprl Lemma : sq_stable__sublist
∀[T:Type]. ∀l1,l2:T List. ((∀x,y:T. Dec(x = y ∈ T)) ⇒ SqStable(l1 ⊆ l2))
Proof
Definitions occuring in Statement :
sublist: 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,
sq_stable: SqStable(P),
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
squash: ↓T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
list_wf,
equal_wf,
decidable_wf,
all_wf,
sublist_wf,
sublist-rec_wf,
squash_wf,
sq_stable__sublist-rec,
sublist-rec-iff-sublist
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
hypothesis,
productElimination,
independent_functionElimination,
addLevel,
imageElimination,
introduction,
because_Cache,
sqequalRule,
imageMemberEquality,
baseClosed,
levelHypothesis,
promote_hyp,
lambdaEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}l1,l2:T List. ((\mforall{}x,y:T. Dec(x = y)) {}\mRightarrow{} SqStable(l1 \msubseteq{} l2))
Date html generated:
2016_05_15-PM-03_34_14
Last ObjectModification:
2016_01_16-AM-10_49_20
Theory : general
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