Nuprl Lemma : monotone_wf

[T,T':Type]. ∀[R:T ⟶ T ⟶ ℙ]. ∀[R':T' ⟶ T' ⟶ ℙ]. ∀[f:T ⟶ T'].  (monotone(T;T';x,y.R[x;y];x,y.R'[x;y];f) ∈ ℙ)


Proof




Definitions occuring in Statement :  monotone: monotone(T;T';x,y.R[x; y];x,y.R'[x; y];f) 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 :  monotone: monotone(T;T';x,y.R[x; y];x,y.R'[x; y];f) uall: [x:A]. B[x] member: t ∈ T so_lambda: λ2x.t[x] implies:  Q prop: so_apply: x[s1;s2] so_apply: x[s]
Lemmas referenced :  all_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality lambdaEquality functionEquality applyEquality hypothesis axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality because_Cache cumulativity universeEquality

Latex:
\mforall{}[T,T':Type].  \mforall{}[R:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].  \mforall{}[R':T'  {}\mrightarrow{}  T'  {}\mrightarrow{}  \mBbbP{}].  \mforall{}[f:T  {}\mrightarrow{}  T'].
    (monotone(T;T';x,y.R[x;y];x,y.R'[x;y];f)  \mmember{}  \mBbbP{})



Date html generated: 2016_05_15-PM-00_03_07
Last ObjectModification: 2015_12_26-PM-11_25_09

Theory : gen_algebra_1


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