Nuprl Lemma : l_tree-definition
∀[L,T,A:Type]. ∀[R:A ─→ l_tree(L;T) ─→ ℙ].
((∀val:L. {x:A| R[x;l_tree_leaf(val)]} )
⇒ (∀val:T. ∀left_subtree,right_subtree:l_tree(L;T).
({x:A| R[x;left_subtree]}
⇒ {x:A| R[x;right_subtree]}
⇒ {x:A| R[x;l_tree_node(val;left_subtree;right_subtree)]} ))
⇒ {∀v:l_tree(L;T). {x:A| R[x;v]} })
Proof
Definitions occuring in Statement :
l_tree_node: l_tree_node(val;left_subtree;right_subtree),
l_tree_leaf: l_tree_leaf(val),
l_tree: l_tree(L;T),
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 :
l_tree-induction,
set_wf,
l_tree_wf,
all_wf,
l_tree_node_wf,
l_tree_leaf_wf
\mforall{}[L,T,A:Type]. \mforall{}[R:A {}\mrightarrow{} l\_tree(L;T) {}\mrightarrow{} \mBbbP{}].
((\mforall{}val:L. \{x:A| R[x;l\_tree\_leaf(val)]\} )
{}\mRightarrow{} (\mforall{}val:T. \mforall{}left$_{subtree}$,right$_{subtree}$:l\_tree(L;T\000C).
(\{x:A| R[x;left$_{subtree}$]\}
{}\mRightarrow{} \{x:A| R[x;right$_{subtree}$]\}
{}\mRightarrow{} \{x:A| R[x;l\_tree\_node(val;left$_{subtree}$;right$_{subtre\000Ce}$)]\} ))
{}\mRightarrow{} \{\mforall{}v:l\_tree(L;T). \{x:A| R[x;v]\} \})
Date html generated:
2015_07_17-AM-07_41_40
Last ObjectModification:
2015_01_27-AM-09_31_14
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