Nuprl Lemma : deq-all-disjoint_wf
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[ass:A List List]. ∀[bs:A List]. (deq-all-disjoint(eq;ass;bs) ∈ 𝔹)
Proof
Definitions occuring in Statement :
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
list: T List,
deq: EqDecider(T),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
bl-all_wf,
list_wf,
deq-disjoint_wf,
l_member_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
setElimination,
rename,
setEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[ass:A List List]. \mforall{}[bs:A List]. (deq-all-disjoint(eq;ass;bs) \mmember{} \mBbbB{})
Date html generated:
2016_05_14-PM-03_24_06
Last ObjectModification:
2015_12_26-PM-06_21_30
Theory : decidable!equality
Home
Index