Nuprl Lemma : deq-member-append
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[L1,L2:A List]. ∀[x:A]. (x ∈b L1 @ L2 ~ x ∈b L1 ∨bx ∈b L2)
Proof
Definitions occuring in Statement :
deq-member: x ∈b L,
append: as @ bs,
list: T List,
deq: EqDecider(T),
bor: p ∨bq,
uall: ∀[x:A]. B[x],
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
all: ∀x:A. B[x],
prop: ℙ,
rev_implies: P ⇐ Q,
sq_type: SQType(T),
guard: {T}
Lemmas referenced :
subtype_base_sq,
bool_subtype_base,
iff_imp_equal_bool,
deq-member_wf,
append_wf,
bor_wf,
iff_transitivity,
assert_wf,
or_wf,
l_member_wf,
iff_weakening_uiff,
assert_of_bor,
assert-deq-member,
member_append,
list_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
because_Cache,
independent_isectElimination,
hypothesis,
hypothesisEquality,
independent_pairFormation,
lambdaFormation,
independent_functionElimination,
dependent_functionElimination,
orFunctionality,
productElimination,
equalityTransitivity,
equalitySymmetry,
sqequalAxiom,
sqequalRule,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[L1,L2:A List]. \mforall{}[x:A]. (x \mmember{}\msubb{} L1 @ L2 \msim{} x \mmember{}\msubb{} L1 \mvee{}\msubb{}x \mmember{}\msubb{} L2)
Date html generated:
2016_05_14-AM-06_53_26
Last ObjectModification:
2015_12_26-PM-00_20_57
Theory : list_0
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