Nuprl Lemma : MultiTree_ind_wf_simple
∀[T,A:Type]. ∀[v:MultiTree(T)]. ∀[Node:labels:{L:Atom List| 0 < ||L||}
⟶ children:({a:Atom| (a ∈ labels)} ⟶ MultiTree(T))
⟶ (u:{a:Atom| (a ∈ labels)} ⟶ A)
⟶ A]. ∀[Leaf:val:T ⟶ A].
(MultiTree_ind(v;
MTree_Node(labels,children)⇒ rec1.Node[labels;children;rec1];
MTree_Leaf(val)⇒ Leaf[val]) ∈ A)
Proof
Definitions occuring in Statement :
MultiTree_ind: MultiTree_ind,
MultiTree: MultiTree(T),
l_member: (x ∈ l),
length: ||as||,
list: T List,
less_than: a < b,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2;s3],
so_apply: x[s],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
natural_number: $n,
atom: Atom,
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],
subtype_rel: A ⊆r B,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
true: True,
guard: {T}
Lemmas referenced :
MultiTree_ind_wf,
true_wf,
MultiTree_wf,
subtype_rel_dep_function,
list_wf,
less_than_wf,
length_wf,
l_member_wf,
set_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
lambdaEquality,
applyEquality,
setEquality,
atomEquality,
natural_numberEquality,
functionEquality,
setElimination,
rename,
because_Cache,
independent_isectElimination,
lambdaFormation,
dependent_set_memberEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T,A:Type]. \mforall{}[v:MultiTree(T)]. \mforall{}[Node:labels:\{L:Atom List| 0 < ||L||\}
{}\mrightarrow{} children:(\{a:Atom| (a \mmember{} labels)\} {}\mrightarrow{} MultiTree(T))
{}\mrightarrow{} (u:\{a:Atom| (a \mmember{} labels)\} {}\mrightarrow{} A)
{}\mrightarrow{} A]. \mforall{}[Leaf:val:T {}\mrightarrow{} A].
(MultiTree\_ind(v;
MTree\_Node(labels,children){}\mRightarrow{} rec1.Node[labels;children;rec1];
MTree\_Leaf(val){}\mRightarrow{} Leaf[val]) \mmember{} A)
Date html generated:
2016_05_16-AM-08_53_49
Last ObjectModification:
2015_12_28-PM-06_53_39
Theory : C-semantics
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