Nuprl Lemma : list-eq-subtype
∀[A:Type]. ∀[d1,d2:A List]. d1 = d2 ∈ ({a:A| (a ∈ d1)} List) supposing d1 = d2 ∈ (A List)
Proof
Definitions occuring in Statement :
l_member: (x ∈ l),
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
set: {x:A| B[x]} ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
prop: ℙ,
so_apply: x[s],
so_lambda: λ2x.t[x],
true: True,
squash: ↓T,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q
Lemmas referenced :
equal_wf,
list_wf,
list-eq-subtype1,
l_member_wf,
list-subtype,
length_wf_nat,
nat_wf,
set_wf,
member_wf,
squash_wf,
true_wf,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
because_Cache,
universeEquality,
isect_memberFormation,
sqequalRule,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lambdaEquality,
independent_isectElimination,
dependent_set_memberEquality,
hyp_replacement,
Error :applyLambdaEquality,
instantiate,
setEquality,
setElimination,
rename,
natural_numberEquality,
applyEquality,
imageElimination,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination
Latex:
\mforall{}[A:Type]. \mforall{}[d1,d2:A List]. d1 = d2 supposing d1 = d2
Date html generated:
2016_10_21-AM-10_01_26
Last ObjectModification:
2016_07_12-AM-05_23_38
Theory : list_1
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