Nuprl Lemma : safety_wf
∀[A:Type]. ∀[P:(A List) ⟶ ℙ]. (safety(A;x.P[x]) ∈ ℙ)
Proof
Definitions occuring in Statement :
safety: safety(A;tr.P[tr]),
list: T List,
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,
safety: safety(A;tr.P[tr]),
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
all_wf,
list_wf,
iseg_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
functionEquality,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionIsType,
universeIsType,
universeEquality,
isect_memberEquality,
cumulativity
Latex:
\mforall{}[A:Type]. \mforall{}[P:(A List) {}\mrightarrow{} \mBbbP{}]. (safety(A;x.P[x]) \mmember{} \mBbbP{})
Date html generated:
2019_10_15-AM-10_54_03
Last ObjectModification:
2018_09_27-AM-09_37_33
Theory : list!
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