Nuprl Lemma : preorder_wf

[T:Type]. ∀[R:T ⟶ T ⟶ ℙ].  (Preorder(T;x,y.R[x;y]) ∈ ℙ)


Proof




Definitions occuring in Statement :  preorder: Preorder(T;x,y.R[x; y]) uall: [x:A]. B[x] prop: 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 preorder: Preorder(T;x,y.R[x; y]) prop: and: P ∧ Q so_lambda: λ2y.t[x; y] so_apply: x[s1;s2]
Lemmas referenced :  refl_wf trans_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :isect_memberFormation_alt,  introduction cut sqequalRule productEquality extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality lambdaEquality applyEquality hypothesis axiomEquality equalityTransitivity equalitySymmetry Error :functionIsType,  Error :universeIsType,  Error :inhabitedIsType,  universeEquality isect_memberEquality functionEquality cumulativity

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



Date html generated: 2019_06_20-PM-00_28_53
Last ObjectModification: 2018_09_26-AM-11_46_38

Theory : rel_1


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