Nuprl Lemma : strict-majority_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[L:T List]. (strict-majority(eq;L) ∈ T?)
Proof
Definitions occuring in Statement :
strict-majority: strict-majority(eq;L),
list: T List,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
unit: Unit,
member: t ∈ T,
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
strict-majority: strict-majority(eq;L),
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
nat_plus: ℕ+,
prop: ℙ,
pi2: snd(t),
implies: P ⇒ Q,
or: P ∨ Q,
ifthenelse: if b then t else f fi ,
btrue: tt,
cons: [a / b],
top: Top,
bfalse: ff
Lemmas referenced :
filter_wf5,
count-repeats_wf,
l_member_wf,
subtype_rel_list,
nat_plus_wf,
subtype_rel_product,
lt_int_wf,
length_wf,
list_wf,
let_wf,
unit_wf2,
list-cases,
null_nil_lemma,
it_wf,
product_subtype_list,
null_cons_lemma,
hd_wf,
cons_wf,
length_cons_ge_one,
top_wf,
pi1_wf,
equal_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
productEquality,
cumulativity,
hypothesisEquality,
intEquality,
because_Cache,
hypothesis,
applyEquality,
sqequalRule,
lambdaEquality,
lambdaFormation,
productElimination,
independent_pairEquality,
independent_isectElimination,
setElimination,
rename,
multiplyEquality,
natural_numberEquality,
setEquality,
unionEquality,
dependent_functionElimination,
unionElimination,
inrEquality,
promote_hyp,
hypothesis_subsumption,
isect_memberEquality,
voidElimination,
voidEquality,
inlEquality,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
axiomEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[L:T List]. (strict-majority(eq;L) \mmember{} T?)
Date html generated:
2017_04_17-AM-09_09_15
Last ObjectModification:
2017_02_27-PM-05_17_26
Theory : decidable!equality
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