Nuprl Lemma : subterm_wf
∀[opr:Type]. ∀[s,t:term(opr)]. (s << t ∈ ℙ)
Proof
Definitions occuring in Statement :
subterm: s << t,
term: term(opr),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subterm: s << t,
infix_ap: x f y
Lemmas referenced :
subterm-rel_wf,
term_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
applyEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType,
instantiate,
universeEquality
Latex:
\mforall{}[opr:Type]. \mforall{}[s,t:term(opr)]. (s << t \mmember{} \mBbbP{})
Date html generated:
2020_05_19-PM-09_54_09
Last ObjectModification:
2020_03_09-PM-04_30_10
Theory : terms
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