Nuprl Lemma : safety_nil
∀[T:Type]. ∀[P:(T List) ⟶ ℙ]. ((∃l:T List. P[l]) ⇒ safety(T;x.P[x]) ⇒ P[[]])
Proof
Definitions occuring in Statement :
safety: safety(A;tr.P[tr]),
nil: [],
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
safety: safety(A;tr.P[tr]),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
exists: ∃x:A. B[x],
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
all: ∀x:A. B[x]
Lemmas referenced :
all_wf,
list_wf,
iseg_wf,
exists_wf,
nil_wf,
nil_iseg
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
cut,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
lambdaEquality,
functionEquality,
applyEquality,
functionIsType,
universeIsType,
universeEquality,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[P:(T List) {}\mrightarrow{} \mBbbP{}]. ((\mexists{}l:T List. P[l]) {}\mRightarrow{} safety(T;x.P[x]) {}\mRightarrow{} P[[]])
Date html generated:
2019_10_15-AM-10_54_12
Last ObjectModification:
2018_09_27-AM-10_02_39
Theory : list!
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