Nuprl Lemma : l-union-same
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[as:T List]. (as ⋃ as ~ as)
Proof
Definitions occuring in Statement :
l-union: as ⋃ bs,
list: T List,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
uimplies: b supposing a
Lemmas referenced :
list_wf,
deq_wf,
l_contains_weakening,
l-union-subset
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
sqequalAxiom,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
isect_memberEquality,
because_Cache,
universeEquality,
dependent_functionElimination,
independent_isectElimination
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[as:T List]. (as \mcup{} as \msim{} as)
Date html generated:
2016_05_14-PM-03_24_42
Last ObjectModification:
2015_12_26-PM-06_21_52
Theory : decidable!equality
Home
Index