Nuprl Lemma : rel_star_monotonic
∀[T:Type]. ∀[R1,R2:T ⟶ T ⟶ ℙ]. ∀x,y:T. (R1 => R2 ⇒ (x (R1^*) y) ⇒ (x (R2^*) y))
Proof
Definitions occuring in Statement :
rel_star: R^*,
rel_implies: R1 => R2,
uall: ∀[x:A]. B[x],
prop: ℙ,
infix_ap: x f y,
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
rel_implies: R1 => R2,
prop: ℙ,
infix_ap: x f y
Lemmas referenced :
rel_star_monotone,
rel_star_wf,
rel_implies_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesisEquality,
independent_functionElimination,
hypothesis,
dependent_functionElimination,
applyEquality,
Error :inhabitedIsType,
Error :functionIsType,
Error :universeIsType,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[R1,R2:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}].
\mforall{}x,y:T. (R1 => R2 {}\mRightarrow{} (x (R1\^{}*) y) {}\mRightarrow{} (x (R2\^{}*) y))
Date html generated:
2019_06_20-PM-00_30_41
Last ObjectModification:
2018_09_26-PM-00_48_04
Theory : relations
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