### Nuprl Lemma : l_tree_leaf_wf

`∀[L,T:Type]. ∀[val:L].  (l_tree_leaf(val) ∈ l_tree(L;T))`

Proof

Definitions occuring in Statement :  l_tree_leaf: `l_tree_leaf(val)` l_tree: `l_tree(L;T)` uall: `∀[x:A]. B[x]` member: `t ∈ T` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` l_tree: `l_tree(L;T)` l_tree_leaf: `l_tree_leaf(val)` eq_atom: `x =a y` ifthenelse: `if b then t else f fi ` btrue: `tt` subtype_rel: `A ⊆r B` ext-eq: `A ≡ B` and: `P ∧ Q` l_treeco_size: `l_treeco_size(p)` l_tree_size: `l_tree_size(p)` has-value: `(a)↓` nat: `ℕ` le: `A ≤ B` less_than': `less_than'(a;b)` false: `False` not: `¬A` implies: `P `` Q` prop: `ℙ` all: `∀x:A. B[x]` so_lambda: `λ2x.t[x]` so_apply: `x[s]` uimplies: `b supposing a`
Lemmas referenced :  l_treeco-ext ifthenelse_wf eq_atom_wf l_treeco_wf false_wf le_wf nat_wf has-value_wf_base set_subtype_base int_subtype_base is-exception_wf equal_wf has-value_wf-partial set-value-type int-value-type l_treeco_size_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation cut dependent_set_memberEquality introduction extract_by_obid hypothesis sqequalHypSubstitution isectElimination thin because_Cache hypothesisEquality sqequalRule dependent_pairEquality tokenEquality instantiate universeEquality productEquality voidEquality applyEquality productElimination natural_numberEquality independent_pairFormation lambdaFormation divergentSqle sqleReflexivity intEquality lambdaEquality independent_isectElimination equalityTransitivity equalitySymmetry dependent_functionElimination independent_functionElimination cumulativity

Latex:
\mforall{}[L,T:Type].  \mforall{}[val:L].    (l\_tree\_leaf(val)  \mmember{}  l\_tree(L;T))

Date html generated: 2018_05_22-PM-09_38_32
Last ObjectModification: 2017_03_04-PM-07_25_19

Theory : labeled!trees

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