Nuprl Lemma : MMTree-definition
∀[T,A:Type]. ∀[R:A ─→ MMTree(T) ─→ ℙ].
((∀val:T. {x:A| R[x;MMTree_Leaf(val)]} )
⇒ (∀forest:MMTree(T) List List. ((∀u∈forest.(∀u1∈u.{x:A| R[x;u1]} )) ⇒ {x:A| R[x;MMTree_Node(forest)]} ))
⇒ {∀v:MMTree(T). {x:A| R[x;v]} })
Proof
Definitions occuring in Statement :
MMTree_Node: MMTree_Node(forest),
MMTree_Leaf: MMTree_Leaf(val),
MMTree: MMTree(T),
l_all: (∀x∈L.P[x]),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
so_apply: x[s1;s2],
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
universe: Type
Lemmas :
MMTree-induction,
set_wf,
all_wf,
list_wf,
MMTree_wf,
l_all_wf2,
l_member_wf,
MMTree_Node_wf,
MMTree_Leaf_wf
\mforall{}[T,A:Type]. \mforall{}[R:A {}\mrightarrow{} MMTree(T) {}\mrightarrow{} \mBbbP{}].
((\mforall{}val:T. \{x:A| R[x;MMTree\_Leaf(val)]\} )
{}\mRightarrow{} (\mforall{}forest:MMTree(T) List List
((\mforall{}u\mmember{}forest.(\mforall{}u1\mmember{}u.\{x:A| R[x;u1]\} )) {}\mRightarrow{} \{x:A| R[x;MMTree\_Node(forest)]\} ))
{}\mRightarrow{} \{\mforall{}v:MMTree(T). \{x:A| R[x;v]\} \})
Date html generated:
2015_07_17-AM-07_47_19
Last ObjectModification:
2015_01_27-AM-09_39_22
Home
Index