Nuprl Lemma : hered-term_wf
∀[opr:Type]. ∀[P:term(opr) ⟶ ℙ]. (hered-term(opr;t.P[t]) ∈ Type)
Proof
Definitions occuring in Statement :
hered-term: hered-term(opr;t.P[t]),
term: term(opr),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
hered-term: hered-term(opr;t.P[t]),
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ
Lemmas referenced :
term_wf,
hereditarily_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
setEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality_alt,
applyEquality,
inhabitedIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionIsType,
universeIsType,
universeEquality,
isect_memberEquality_alt,
isectIsTypeImplies,
instantiate
Latex:
\mforall{}[opr:Type]. \mforall{}[P:term(opr) {}\mrightarrow{} \mBbbP{}]. (hered-term(opr;t.P[t]) \mmember{} Type)
Date html generated:
2020_05_19-PM-09_54_40
Last ObjectModification:
2020_03_10-AM-11_24_09
Theory : terms
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