### Nuprl Lemma : cWO-rel_wf

`∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ].  (cWO-rel(R) ∈ n:ℕ ⟶ (ℕn ⟶ (T?)) ⟶ (T?) ⟶ ℙ)`

Proof

Definitions occuring in Statement :  cWO-rel: `cWO-rel(R)` int_seg: `{i..j-}` nat: `ℕ` uall: `∀[x:A]. B[x]` prop: `ℙ` unit: `Unit` member: `t ∈ T` function: `x:A ⟶ B[x]` union: `left + right` natural_number: `\$n` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` cWO-rel: `cWO-rel(R)` implies: `P `` Q` prop: `ℙ` and: `P ∧ Q` nat: `ℕ` int_seg: `{i..j-}` lelt: `i ≤ j < k` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` iff: `P `⇐⇒` Q` not: `¬A` rev_implies: `P `` Q` false: `False` uiff: `uiff(P;Q)` uimplies: `b supposing a` subtract: `n - m` subtype_rel: `A ⊆r B` le: `A ≤ B` less_than': `less_than'(a;b)` true: `True` outl: `outl(x)` isl: `isl(x)` assert: `↑b` ifthenelse: `if b then t else f fi ` bfalse: `ff`
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lambdaEquality functionEquality productEquality lemma_by_obid sqequalHypSubstitution isectElimination thin natural_numberEquality setElimination rename hypothesisEquality hypothesis cumulativity applyEquality productElimination dependent_set_memberEquality independent_pairFormation dependent_functionElimination unionElimination lambdaFormation voidElimination independent_functionElimination independent_isectElimination addEquality because_Cache minusEquality universeEquality unionEquality axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality

Latex:
\mforall{}[T:Type].  \mforall{}[R:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].    (cWO-rel(R)  \mmember{}  n:\mBbbN{}  {}\mrightarrow{}  (\mBbbN{}n  {}\mrightarrow{}  (T?))  {}\mrightarrow{}  (T?)  {}\mrightarrow{}  \mBbbP{})

Date html generated: 2016_05_13-PM-03_52_09
Last ObjectModification: 2015_12_26-AM-10_17_05

Theory : bar-induction

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