Nuprl Lemma : transitive-closure-minimal-ext
∀[A:Type]. ∀[R,Q:A ⟶ A ⟶ ℙ]. (R => Q ⇒ Trans(A;x,y.x Q y) ⇒ TC(R) => Q)
Proof
Definitions occuring in Statement :
transitive-closure: TC(R),
rel_implies: R1 => R2,
trans: Trans(T;x,y.E[x; y]),
uall: ∀[x:A]. B[x],
prop: ℙ,
infix_ap: x f y,
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
spreadn: spread3,
transitive-closure-minimal
Lemmas referenced :
transitive-closure-minimal
Rules used in proof :
introduction,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
instantiate,
extract_by_obid,
hypothesis,
sqequalRule,
thin,
sqequalHypSubstitution,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[A:Type]. \mforall{}[R,Q:A {}\mrightarrow{} A {}\mrightarrow{} \mBbbP{}]. (R => Q {}\mRightarrow{} Trans(A;x,y.x Q y) {}\mRightarrow{} TC(R) => Q)
Date html generated:
2018_05_21-PM-00_51_42
Last ObjectModification:
2018_05_19-AM-06_40_14
Theory : relations2
Home
Index