### 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: `ℙ` 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: `P `` Q` prop: `ℙ` 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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