Nuprl Lemma : oobboth?_wf
∀[A,B:Type]. ∀[x:one_or_both(A;B)]. (oobboth?(x) ∈ 𝔹)
Proof
Definitions occuring in Statement :
oobboth?: oobboth?(x),
one_or_both: one_or_both(A;B),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
oobboth?: oobboth?(x),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
top: Top,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
one_or_both_ind_wf,
bool_wf,
top_wf,
oob-subtype,
btrue_wf,
bfalse_wf,
one_or_both_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesis,
hypothesisEquality,
applyEquality,
because_Cache,
independent_isectElimination,
lambdaEquality,
isect_memberEquality,
voidElimination,
voidEquality,
productEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[x:one\_or\_both(A;B)]. (oobboth?(x) \mmember{} \mBbbB{})
Date html generated:
2016_05_15-PM-05_33_34
Last ObjectModification:
2015_12_27-PM-02_08_43
Theory : general
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