Nuprl Lemma : xxtrans_wf

[T:Type]. ∀[E:T ⟶ T ⟶ ℙ].  (trans(T;E) ∈ ℙ)


Proof




Definitions occuring in Statement :  xxtrans: trans(T;E) uall: [x:A]. B[x] prop: member: t ∈ T function: x:A ⟶ B[x] universe: Type
Definitions unfolded in proof :  xxtrans: trans(T;E) uall: [x:A]. B[x] member: t ∈ T so_lambda: λ2y.t[x; y] so_apply: x[s1;s2] prop:
Lemmas referenced :  trans_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut 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{}[E:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].    (trans(T;E)  \mmember{}  \mBbbP{})



Date html generated: 2016_05_15-PM-00_00_53
Last ObjectModification: 2015_12_26-PM-11_26_31

Theory : gen_algebra_1


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