Nuprl Lemma : rel-connected_transitivity
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. ∀[x,y,z:T]. (x──R⟶y ⇒ y──R⟶z ⇒ x──R⟶z)
Proof
Definitions occuring in Statement :
rel-connected: x──R⟶y,
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
rel-connected: x──R⟶y,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
infix_ap: x f y
Lemmas referenced :
rel_star_transitivity,
rel_star_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesisEquality,
independent_functionElimination,
hypothesis,
applyEquality,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. \mforall{}[x,y,z:T]. (x{}{}R{}\mrightarrow{}y {}\mRightarrow{} y{}{}R{}\mrightarrow{}z {}\mRightarrow{} x{}{}R{}\mrightarrow{}z)
Date html generated:
2016_05_13-PM-04_19_18
Last ObjectModification:
2015_12_26-AM-11_33_39
Theory : relations
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