### Nuprl Lemma : wellfounded_wf

`∀[A:Type]. ∀[r:A ⟶ A ⟶ ℙ].  (WellFnd{i}(A;x,y.r[x;y]) ∈ ℙ')`

Proof

Definitions occuring in Statement :  wellfounded: `WellFnd{i}(A;x,y.R[x; y])` uall: `∀[x:A]. B[x]` prop: `ℙ` so_apply: `x[s1;s2]` member: `t ∈ T` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` wellfounded: `WellFnd{i}(A;x,y.R[x; y])` prop: `ℙ` so_lambda: `λ2x.t[x]` implies: `P `` Q` so_apply: `x[s1;s2]` so_apply: `x[s]` guard: `{T}`
Lemmas referenced :  uall_wf all_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :isect_memberFormation_alt,  introduction cut sqequalRule thin instantiate extract_by_obid sqequalHypSubstitution isectElimination functionEquality cumulativity hypothesisEquality universeEquality lambdaEquality applyEquality hypothesis axiomEquality equalityTransitivity equalitySymmetry Error :functionIsType,  Error :universeIsType,  Error :inhabitedIsType,  isect_memberEquality

Latex:
\mforall{}[A:Type].  \mforall{}[r:A  {}\mrightarrow{}  A  {}\mrightarrow{}  \mBbbP{}].    (WellFnd\{i\}(A;x,y.r[x;y])  \mmember{}  \mBbbP{}')

Date html generated: 2019_06_20-AM-11_19_11
Last ObjectModification: 2018_09_26-AM-10_41_44

Theory : well_fnd

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