Nuprl Lemma : immediate-is-subterm
∀[opr:Type]. ∀s,t:term(opr). (s < t ⇒ s << t)
Proof
Definitions occuring in Statement :
subterm: s << t,
immediate-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 :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
subterm: s << t,
member: t ∈ T,
subterm-rel: subterm-rel(opr),
rel_implies: R1 => R2,
infix_ap: x f y,
prop: ℙ,
guard: {T}
Lemmas referenced :
transitive-closure-contains,
immediate-subterm_wf,
term_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
lambdaEquality_alt,
hypothesisEquality,
hypothesis,
inhabitedIsType,
sqequalRule,
universeIsType,
instantiate,
universeEquality,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[opr:Type]. \mforall{}s,t:term(opr). (s < t {}\mRightarrow{} s << t)
Date html generated:
2020_05_19-PM-09_54_11
Last ObjectModification:
2020_03_10-PM-01_42_33
Theory : terms
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