Nuprl Lemma : bs_tree_ind_wf_simple
∀[E,A:Type]. ∀[v:bs_tree(E)]. ∀[null:A]. ∀[leaf:value:E ⟶ A]. ∀[node:left:bs_tree(E)
⟶ value:E
⟶ right:bs_tree(E)
⟶ A
⟶ A
⟶ A].
(case(v)
null=>null
leaf(value)=>leaf[value]
node(left,value,right)=>rec1,rec2.node[left;value;right;rec1;rec2] ∈ A)
Proof
Definitions occuring in Statement :
bs_tree_ind: bs_tree_ind,
bs_tree: bs_tree(E),
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2;s3;s4;s5],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
true: True,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
guard: {T}
Lemmas referenced :
set_wf,
subtype_rel_dep_function,
bs_tree_wf,
true_wf,
bs_tree_ind_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
lambdaEquality,
cumulativity,
dependent_set_memberEquality,
natural_numberEquality,
functionExtensionality,
applyEquality,
because_Cache,
functionEquality,
setEquality,
independent_isectElimination,
lambdaFormation,
setElimination,
rename,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[E,A:Type]. \mforall{}[v:bs\_tree(E)]. \mforall{}[null:A]. \mforall{}[leaf:value:E {}\mrightarrow{} A]. \mforall{}[node:left:bs\_tree(E)
{}\mrightarrow{} value:E
{}\mrightarrow{} right:bs\_tree(E)
{}\mrightarrow{} A
{}\mrightarrow{} A
{}\mrightarrow{} A].
(case(v)
null=>null
leaf(value)=>leaf[value]
node(left,value,right)=>rec1,rec2.node[left;value;right;rec1;rec2] \mmember{} A)
Date html generated:
2016_05_15-PM-01_51_03
Last ObjectModification:
2016_04_07-PM-02_27_12
Theory : tree_1
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