Nuprl Lemma : rel-monotone_wf
∀[T:Type]. ∀[F:(T ⟶ T ⟶ ℙ) ⟶ T ⟶ T ⟶ ℙ]. (rel-monotone{i:l}(T;R.F[R]) ∈ ℙ')
Proof
Definitions occuring in Statement :
rel-monotone: rel-monotone{i:l}(T;R.F[R]),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rel-monotone: rel-monotone{i:l}(T;R.F[R]),
prop: ℙ,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
so_apply: x[s]
Lemmas referenced :
all_wf,
rel_implies_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
functionEquality,
cumulativity,
hypothesisEquality,
universeEquality,
lambdaEquality,
hypothesis,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[T:Type]. \mforall{}[F:(T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}) {}\mrightarrow{} T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. (rel-monotone\{i:l\}(T;R.F[R]) \mmember{} \mBbbP{}')
Date html generated:
2016_05_14-AM-06_04_56
Last ObjectModification:
2015_12_26-AM-11_33_01
Theory : relations
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