Nuprl Lemma : decidable__sublist-rec
∀[T:Type]. ∀l1,l2:T List. ((∀x,y:T. Dec(x = y ∈ T)) ⇒ Dec(sublist-rec(T;l1;l2)))
Proof
Definitions occuring in Statement :
sublist-rec: sublist-rec(T;l1;l2),
list: T List,
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,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
or: P ∨ Q,
sublist-rec: sublist-rec(T;l1;l2),
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
cons: [a / b],
decidable: Dec(P),
guard: {T},
and: P ∧ Q,
cand: A c∧ B,
not: ¬A,
false: False,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
list_induction,
all_wf,
list_wf,
decidable_wf,
sublist-rec_wf,
equal_wf,
list-cases,
list_ind_nil_lemma,
decidable__true,
product_subtype_list,
list_ind_cons_lemma,
decidable__false,
cons_wf,
and_wf,
not_wf,
or_wf,
nil_wf,
true_wf,
decidable_functionality,
iff_weakening_uiff,
sublist-rec-nil-iff
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
thin,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
hypothesis,
independent_functionElimination,
because_Cache,
rename,
dependent_functionElimination,
universeEquality,
unionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
promote_hyp,
hypothesis_subsumption,
productElimination,
inlFormation,
inrFormation,
independent_pairFormation
Latex:
\mforall{}[T:Type]. \mforall{}l1,l2:T List. ((\mforall{}x,y:T. Dec(x = y)) {}\mRightarrow{} Dec(sublist-rec(T;l1;l2)))
Date html generated:
2016_05_15-PM-03_34_06
Last ObjectModification:
2015_12_27-PM-01_13_14
Theory : general
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