Nuprl Lemma : rel_star_functionality_wrt_rel_implies
∀[T:Type]. ∀[R1,R2:T ⟶ T ⟶ ℙ]. (R1 => R2 ⇒ R1^* => R2^*)
Proof
Definitions occuring in Statement :
rel_star: R^*,
rel_implies: R1 => R2,
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
rel_implies: R1 => R2,
all: ∀x:A. B[x],
member: t ∈ T,
infix_ap: x f y,
subtype_rel: A ⊆r B,
prop: ℙ,
guard: {T}
Lemmas referenced :
rel_star_monotonic,
rel_star_wf,
subtype_rel_self,
rel_implies_wf,
istype-universe
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
Error :lambdaFormation_alt,
Error :universeIsType,
applyEquality,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
instantiate,
universeEquality,
because_Cache,
Error :inhabitedIsType,
Error :functionIsType,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[R1,R2:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. (R1 => R2 {}\mRightarrow{} rel\_star(T; R1) => rel\_star(T; R2))
Date html generated:
2019_06_20-PM-02_02_22
Last ObjectModification:
2019_01_17-PM-10_04_01
Theory : relations2
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