### Nuprl Lemma : l_treeco_size_wf

`∀[L,T:Type]. ∀[p:l_treeco(L;T)].  (l_treeco_size(p) ∈ partial(ℕ))`

Proof

Definitions occuring in Statement :  l_treeco_size: `l_treeco_size(p)` l_treeco: `l_treeco(L;T)` partial: `partial(T)` nat: `ℕ` uall: `∀[x:A]. B[x]` member: `t ∈ T` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` nat: `ℕ` so_lambda: `λ2x.t[x]` so_apply: `x[s]` continuous-monotone: `ContinuousMonotone(T.F[T])` and: `P ∧ Q` type-monotone: `Monotone(T.F[T])` subtype_rel: `A ⊆r B` all: `∀x:A. B[x]` implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` ifthenelse: `if b then t else f fi ` bfalse: `ff` exists: `∃x:A. B[x]` prop: `ℙ` or: `P ∨ Q` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` assert: `↑b` false: `False` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]` strong-type-continuous: `Continuous+(T.F[T])` type-continuous: `Continuous(T.F[T])` l_treeco: `l_treeco(L;T)` eq_atom: `x =a y` le: `A ≤ B` less_than': `less_than'(a;b)` not: `¬A` spreadn: spread3 l_treeco_size: `l_treeco_size(p)`
Lemmas referenced :  fix_wf_corec-partial1 nat_wf set-value-type le_wf int-value-type nat-mono ifthenelse_wf eq_atom_wf subtype_rel_product bool_wf eqtt_to_assert assert_of_eq_atom eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot neg_assert_of_eq_atom subtype_rel_wf strong-continuous-depproduct continuous-constant strong-continuous-product continuous-id subtype_rel_weakening atom_subtype_base false_wf inclusion-partial add-wf-partial-nat partial_wf l_treeco_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin hypothesis independent_isectElimination sqequalRule intEquality lambdaEquality natural_numberEquality hypothesisEquality productEquality atomEquality instantiate tokenEquality universeEquality cumulativity voidEquality independent_pairFormation because_Cache lambdaFormation unionElimination equalityElimination productElimination dependent_pairFormation equalityTransitivity equalitySymmetry promote_hyp dependent_functionElimination independent_functionElimination voidElimination axiomEquality isect_memberEquality isectEquality applyEquality functionExtensionality functionEquality dependent_set_memberEquality

Latex:
\mforall{}[L,T:Type].  \mforall{}[p:l\_treeco(L;T)].    (l\_treeco\_size(p)  \mmember{}  partial(\mBbbN{}))

Date html generated: 2018_05_22-PM-09_38_21
Last ObjectModification: 2017_03_04-PM-07_25_32

Theory : labeled!trees

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