Nuprl Lemma : oob-getright?_wf
∀[B,A:Type]. ∀[x:one_or_both(A;B)]. (oob-getright?(x) ∈ bag(B))
Proof
Definitions occuring in Statement :
oob-getright?: oob-getright?(x),
one_or_both: one_or_both(A;B),
bag: bag(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
oob-getright?: oob-getright?(x),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
prop: ℙ,
bfalse: ff
Lemmas referenced :
oob-hasright_wf,
bool_wf,
eqtt_to_assert,
single-bag_wf,
oob-getright_wf,
assert_wf,
uiff_transitivity,
equal-wf-T-base,
bnot_wf,
not_wf,
eqff_to_assert,
assert_of_bnot,
empty-bag_wf,
equal_wf,
one_or_both_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
lambdaFormation,
unionElimination,
equalityElimination,
because_Cache,
productElimination,
independent_isectElimination,
dependent_functionElimination,
dependent_set_memberEquality,
equalityTransitivity,
equalitySymmetry,
baseClosed,
independent_functionElimination,
axiomEquality,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[B,A:Type]. \mforall{}[x:one\_or\_both(A;B)]. (oob-getright?(x) \mmember{} bag(B))
Date html generated:
2018_05_21-PM-08_59_34
Last ObjectModification:
2017_07_26-PM-06_23_01
Theory : general
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