### Nuprl Lemma : W-rel_wf

`∀[A:Type]. ∀[B:A ⟶ Type]. ∀[w:W(A;a.B[a])].`
`  (W-rel(A;a.B[a];w) ∈ n:ℕ ⟶ (ℕn ⟶ cw-step(A;a.B[a])) ⟶ cw-step(A;a.B[a]) ⟶ ℙ)`

Proof

Definitions occuring in Statement :  W-rel: `W-rel(A;a.B[a];w)` W: `W(A;a.B[a])` cw-step: `cw-step(A;a.B[a])` int_seg: `{i..j-}` nat: `ℕ` uall: `∀[x:A]. B[x]` prop: `ℙ` so_apply: `x[s]` member: `t ∈ T` function: `x:A ⟶ B[x]` natural_number: `\$n` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` W-rel: `W-rel(A;a.B[a];w)` so_lambda: `λ2x.t[x]` so_apply: `x[s]` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]` so_lambda: `so_lambda(x,y,z.t[x; y; z])` so_apply: `x[s1;s2;s3]` W: `W(A;a.B[a])` subtype_rel: `A ⊆r B` cw-step: `cw-step(A;a.B[a])` nat: `ℕ` prop: `ℙ`
Lemmas referenced :  param-W-rel_wf unit_wf2 it_wf nat_wf int_seg_wf pcw-step_wf W_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesis sqequalRule lambdaEquality hypothesisEquality applyEquality functionEquality cumulativity natural_numberEquality setElimination rename universeEquality axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality because_Cache

Latex:
\mforall{}[A:Type].  \mforall{}[B:A  {}\mrightarrow{}  Type].  \mforall{}[w:W(A;a.B[a])].
(W-rel(A;a.B[a];w)  \mmember{}  n:\mBbbN{}  {}\mrightarrow{}  (\mBbbN{}n  {}\mrightarrow{}  cw-step(A;a.B[a]))  {}\mrightarrow{}  cw-step(A;a.B[a])  {}\mrightarrow{}  \mBbbP{})

Date html generated: 2016_05_14-AM-06_15_02
Last ObjectModification: 2015_12_26-PM-00_05_13

Theory : co-recursion

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