Nuprl Lemma : bs_l_tree_member_wf
∀[L,T:Type]. ∀[t:l_tree(L;T)]. ∀[x:T]. ∀[f:T ⟶ ℤ]. (bs_l_tree_member(x;t;f) ∈ 𝔹)
Proof
Definitions occuring in Statement :
bs_l_tree_member: bs_l_tree_member(x;t;f),
l_tree: l_tree(L;T),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bs_l_tree_member: bs_l_tree_member(x;t;f),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
top: Top,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: so_lambda(x,y,z,w,v.t[x; y; z; w; v]),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff,
prop: ℙ,
so_apply: x[s1;s2;s3;s4;s5]
Lemmas referenced :
l_tree_ind_wf_simple,
top_wf,
bool_wf,
l_tree_covariant,
btrue_wf,
bor_wf,
eq_int_wf,
lt_int_wf,
equal_wf,
l_tree_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
cumulativity,
hypothesisEquality,
applyEquality,
independent_isectElimination,
lambdaEquality,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
functionExtensionality,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
functionEquality,
intEquality,
universeEquality
Latex:
\mforall{}[L,T:Type]. \mforall{}[t:l\_tree(L;T)]. \mforall{}[x:T]. \mforall{}[f:T {}\mrightarrow{} \mBbbZ{}]. (bs\_l\_tree\_member(x;t;f) \mmember{} \mBbbB{})
Date html generated:
2018_05_22-PM-09_40_02
Last ObjectModification:
2017_03_04-PM-07_25_36
Theory : labeled!trees
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