Nuprl Lemma : hereditarily_functionality_wrt_subterm
∀[opr:Type]. ∀[P:term(opr) ⟶ ℙ]. ∀t,s:term(opr). (s << t ⇒ hereditarily(opr;s.P[s];t) ⇒ hereditarily(opr;s.P[s];s))
Proof
Definitions occuring in Statement :
hereditarily: hereditarily(opr;s.P[s];t),
subterm: s << t,
term: term(opr),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
hereditarily: hereditarily(opr;s.P[s];t),
and: P ∧ Q,
cand: A c∧ B,
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T}
Lemmas referenced :
subterm_transitivity,
subterm_wf,
hereditarily_wf,
term_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
lambdaFormation_alt,
sqequalHypSubstitution,
productElimination,
thin,
cut,
independent_pairFormation,
hypothesis,
dependent_functionElimination,
hypothesisEquality,
independent_functionElimination,
introduction,
extract_by_obid,
isectElimination,
universeIsType,
because_Cache,
sqequalRule,
lambdaEquality_alt,
applyEquality,
inhabitedIsType,
functionIsType,
universeEquality,
instantiate
Latex:
\mforall{}[opr:Type]. \mforall{}[P:term(opr) {}\mrightarrow{} \mBbbP{}].
\mforall{}t,s:term(opr). (s << t {}\mRightarrow{} hereditarily(opr;s.P[s];t) {}\mRightarrow{} hereditarily(opr;s.P[s];s))
Date html generated:
2020_05_19-PM-09_54_34
Last ObjectModification:
2020_03_10-PM-01_24_28
Theory : terms
Home
Index