Nuprl Lemma : hereditarily_wf
∀[opr:Type]. ∀[P:term(opr) ⟶ ℙ]. ∀[t:term(opr)]. (hereditarily(opr;s.P[s];t) ∈ ℙ)
Proof
Definitions occuring in Statement :
hereditarily: hereditarily(opr;s.P[s];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,
hereditarily: hereditarily(opr;s.P[s];t),
prop: ℙ,
and: P ∧ Q,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q
Lemmas referenced :
term_wf,
subterm_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
productEquality,
applyEquality,
sqequalHypSubstitution,
hypothesisEquality,
functionEquality,
extract_by_obid,
isectElimination,
thin,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
functionIsType,
universeEquality,
instantiate
Latex:
\mforall{}[opr:Type]. \mforall{}[P:term(opr) {}\mrightarrow{} \mBbbP{}]. \mforall{}[t:term(opr)]. (hereditarily(opr;s.P[s];t) \mmember{} \mBbbP{})
Date html generated:
2020_05_19-PM-09_54_33
Last ObjectModification:
2020_03_10-AM-11_23_01
Theory : terms
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