Nuprl Lemma : fix_wf_corec-alt-proof

`∀[F:Type ⟶ Type]. ∀[G:⋂T:Type. (T ⟶ F[T])].  (fix(G) ∈ corec(T.F[T]))`

Proof

Definitions occuring in Statement :  corec: `corec(T.F[T])` uall: `∀[x:A]. B[x]` so_apply: `x[s]` member: `t ∈ T` fix: `fix(F)` isect: `⋂x:A. B[x]` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` so_lambda: `λ2x.t[x]` so_apply: `x[s]` subtype_rel: `A ⊆r B`
Lemmas referenced :  fix_wf_corec
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin sqequalRule lambdaEquality applyEquality hypothesisEquality universeEquality isect_memberEquality equalityTransitivity equalitySymmetry hypothesis isectEquality cumulativity functionEquality axiomEquality because_Cache

Latex:
\mforall{}[F:Type  {}\mrightarrow{}  Type].  \mforall{}[G:\mcap{}T:Type.  (T  {}\mrightarrow{}  F[T])].    (fix(G)  \mmember{}  corec(T.F[T]))

Date html generated: 2016_05_14-AM-06_19_15
Last ObjectModification: 2015_12_26-PM-00_02_26

Theory : co-recursion

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