Nuprl Lemma : subterm_transitivity
∀[opr:Type]. ∀s,t,r:term(opr). (s << t ⇒ t << r ⇒ s << r)
Proof
Definitions occuring in Statement :
subterm: s << t,
term: term(opr),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
subterm: s << t,
subterm-rel: subterm-rel(opr),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
infix_ap: x f y,
prop: ℙ,
guard: {T},
utrans: UniformlyTrans(T;x,y.E[x; y])
Lemmas referenced :
transitive-closure-transitive,
immediate-subterm_wf,
transitive-closure_wf,
term_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
lambdaEquality_alt,
hypothesisEquality,
hypothesis,
inhabitedIsType,
universeIsType,
applyEquality,
instantiate,
universeEquality,
independent_functionElimination
Latex:
\mforall{}[opr:Type]. \mforall{}s,t,r:term(opr). (s << t {}\mRightarrow{} t << r {}\mRightarrow{} s << r)
Date html generated:
2020_05_19-PM-09_54_10
Last ObjectModification:
2020_03_10-PM-01_23_24
Theory : terms
Home
Index