### Nuprl Lemma : strongwf-implies

`∀[T:Type]. ∀[R:T ⟶ T ⟶ Type].  (SWellFounded(R[x;y]) `` WellFnd{i}(T;x,y.R[x;y]))`

Proof

Definitions occuring in Statement :  strongwellfounded: `SWellFounded(R[x; y])` wellfounded: `WellFnd{i}(A;x,y.R[x; y])` uall: `∀[x:A]. B[x]` so_apply: `x[s1;s2]` implies: `P `` Q` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  wellfounded: `WellFnd{i}(A;x,y.R[x; y])` strongwellfounded: `SWellFounded(R[x; y])` uall: `∀[x:A]. B[x]` implies: `P `` Q` guard: `{T}` exists: `∃x:A. B[x]` member: `t ∈ T` prop: `ℙ` so_lambda: `λ2x.t[x]` so_apply: `x[s1;s2]` subtype_rel: `A ⊆r B` so_apply: `x[s]` nat: `ℕ` all: `∀x:A. B[x]` int_seg: `{i..j-}` lelt: `i ≤ j < k` and: `P ∧ Q` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` false: `False` not: `¬A` top: `Top` decidable: `Dec(P)` or: `P ∨ Q` le: `A ≤ B` less_than': `less_than'(a;b)` ge: `i ≥ j ` less_than: `a < b` squash: `↓T`
Lemmas referenced :  all_wf exists_wf nat_wf less_than_wf int_seg_properties satisfiable-full-omega-tt intformand_wf intformless_wf itermVar_wf itermConstant_wf intformle_wf int_formula_prop_and_lemma int_formula_prop_less_lemma int_term_value_var_lemma int_term_value_constant_lemma int_formula_prop_le_lemma int_formula_prop_wf int_seg_wf decidable__equal_int subtract_wf int_seg_subtype false_wf decidable__le intformnot_wf itermSubtract_wf intformeq_wf int_formula_prop_not_lemma int_term_value_subtract_lemma int_formula_prop_eq_lemma le_wf equal_wf int_seg_subtype_nat decidable__lt lelt_wf set_wf primrec-wf2 nat_properties itermAdd_wf int_term_value_add_lemma
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation lambdaFormation sqequalHypSubstitution productElimination thin cut introduction extract_by_obid isectElimination cumulativity hypothesisEquality lambdaEquality functionEquality applyEquality functionExtensionality hypothesis universeEquality because_Cache setElimination rename natural_numberEquality independent_isectElimination dependent_pairFormation int_eqEquality intEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll unionElimination addLevel equalityTransitivity equalitySymmetry applyLambdaEquality levelHypothesis hypothesis_subsumption dependent_set_memberEquality independent_functionElimination addEquality imageElimination

Latex:
\mforall{}[T:Type].  \mforall{}[R:T  {}\mrightarrow{}  T  {}\mrightarrow{}  Type].    (SWellFounded(R[x;y])  {}\mRightarrow{}  WellFnd\{i\}(T;x,y.R[x;y]))

Date html generated: 2017_04_17-AM-09_26_36
Last ObjectModification: 2017_02_27-PM-05_27_54

Theory : relations2

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