### Nuprl Lemma : wellfounded-acyclic-rel

`∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ].  (SWellFounded(x R y) `` acyclic-rel(T;R))`

Proof

Definitions occuring in Statement :  acyclic-rel: `acyclic-rel(T;R)` strongwellfounded: `SWellFounded(R[x; y])` uall: `∀[x:A]. B[x]` prop: `ℙ` infix_ap: `x f y` implies: `P `` Q` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` implies: `P `` Q` prop: `ℙ` so_lambda: `λ2x y.t[x; y]` infix_ap: `x f y` subtype_rel: `A ⊆r B` so_apply: `x[s1;s2]` acyclic-rel: `acyclic-rel(T;R)` all: `∀x:A. B[x]` not: `¬A` false: `False` strongwellfounded: `SWellFounded(R[x; y])` exists: `∃x:A. B[x]` less_than: `a < b` squash: `↓T` and: `P ∧ Q` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` top: `Top`
Lemmas referenced :  int_formula_prop_wf int_term_value_var_lemma int_formula_prop_less_lemma itermVar_wf intformless_wf satisfiable-full-omega-tt rel_plus_wf strongwellfounded_wf rel_plus_strongwellfounded
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lambdaFormation lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality independent_functionElimination hypothesis sqequalRule lambdaEquality applyEquality universeEquality dependent_functionElimination because_Cache functionEquality cumulativity isect_memberEquality voidElimination productElimination imageElimination natural_numberEquality independent_isectElimination dependent_pairFormation int_eqEquality intEquality voidEquality computeAll

Latex:
\mforall{}[T:Type].  \mforall{}[R:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].    (SWellFounded(x  R  y)  {}\mRightarrow{}  acyclic-rel(T;R))

Date html generated: 2016_05_14-PM-03_53_30
Last ObjectModification: 2016_01_14-PM-11_10_38

Theory : relations2

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