Nuprl Lemma : union-contains
∀[T:Type]. ∀eq:EqDecider(T). ∀as,bs:T List. as ⊆ as ⋃ bs
Proof
Definitions occuring in Statement :
l-union: as ⋃ bs,
l_contains: A ⊆ B,
list: T List,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
l_contains: A ⊆ B,
member: t ∈ T,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
or: P ∨ Q
Lemmas referenced :
l_all_iff,
l_member_wf,
l-union_wf,
member-union,
list_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
sqequalRule,
lambdaEquality,
setElimination,
rename,
hypothesis,
setEquality,
productElimination,
independent_functionElimination,
because_Cache,
inlFormation,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}eq:EqDecider(T). \mforall{}as,bs:T List. as \msubseteq{} as \mcup{} bs
Date html generated:
2019_06_20-PM-01_55_02
Last ObjectModification:
2018_08_24-PM-11_26_43
Theory : decidable!equality
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