### Nuprl Lemma : decidable-non-minimal_wf

`∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ].  (decidable-non-minimal(T;x,y.R[x;y]) ∈ ℙ)`

Proof

Definitions occuring in Statement :  decidable-non-minimal: `decidable-non-minimal(T;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` decidable-non-minimal: `decidable-non-minimal(T;x,y.R[x; y])` so_lambda: `λ2x.t[x]` so_apply: `x[s1;s2]` so_apply: `x[s]` prop: `ℙ`
Lemmas referenced :  all_wf decidable_wf squash_wf exists_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality lambdaEquality applyEquality hypothesis axiomEquality equalityTransitivity equalitySymmetry functionEquality cumulativity universeEquality isect_memberEquality because_Cache

Latex:
\mforall{}[T:Type].  \mforall{}[R:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].    (decidable-non-minimal(T;x,y.R[x;y])  \mmember{}  \mBbbP{})

Date html generated: 2016_05_15-PM-07_51_09
Last ObjectModification: 2015_12_27-AM-11_05_46

Theory : general

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