### Nuprl Lemma : wfd-tree-rec_wf

`∀[X,T:Type]. ∀[b:X]. ∀[F:(T ⟶ X) ⟶ X]. ∀[t:wfd-tree(T)].  (wfd-tree-rec(b;r.F[r];t) ∈ X)`

Proof

Definitions occuring in Statement :  wfd-tree-rec: `wfd-tree-rec(b;r.F[r];t)` wfd-tree: `wfd-tree(T)` uall: `∀[x:A]. B[x]` so_apply: `x[s]` member: `t ∈ T` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  wfd-tree: `wfd-tree(T)` uall: `∀[x:A]. B[x]` member: `t ∈ T` wfd-tree-rec: `wfd-tree-rec(b;r.F[r];t)` so_lambda: `λ2x.t[x]` all: `∀x:A. B[x]` implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` ifthenelse: `if b then t else f fi ` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` bfalse: `ff` prop: `ℙ` so_apply: `x[s]` so_lambda: `so_lambda(x,y,z.t[x; y; z])` exists: `∃x:A. B[x]` or: `P ∨ Q` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` assert: `↑b` false: `False` so_apply: `x[s1;s2;s3]`
Lemmas referenced :  W-rec_wf bool_wf eqtt_to_assert equal_wf eqff_to_assert bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot W_wf ifthenelse_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin cumulativity hypothesisEquality hypothesis lambdaEquality lambdaFormation unionElimination equalityElimination productElimination independent_isectElimination voidEquality equalityTransitivity equalitySymmetry dependent_functionElimination independent_functionElimination because_Cache dependent_pairFormation promote_hyp instantiate voidElimination applyEquality functionExtensionality functionEquality axiomEquality universeEquality isect_memberEquality

Latex:
\mforall{}[X,T:Type].  \mforall{}[b:X].  \mforall{}[F:(T  {}\mrightarrow{}  X)  {}\mrightarrow{}  X].  \mforall{}[t:wfd-tree(T)].    (wfd-tree-rec(b;r.F[r];t)  \mmember{}  X)

Date html generated: 2017_04_14-AM-07_45_11
Last ObjectModification: 2017_02_27-PM-03_16_11

Theory : co-recursion

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