Nuprl Lemma : sqequal-null
∀[T:Type]. ∀[l:T List]. l ~ [] supposing ↑null(l)
Proof
Definitions occuring in Statement :
null: null(as),
nil: [],
list: T List,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
uiff: uiff(P;Q),
and: P ∧ Q
Lemmas referenced :
sqequal-nil,
assert_wf,
null_wf,
list_wf,
assert_of_null
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
axiomSqEquality,
Error :universeIsType,
sqequalRule,
Error :isect_memberEquality_alt,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality,
productElimination
Latex:
\mforall{}[T:Type]. \mforall{}[l:T List]. l \msim{} [] supposing \muparrow{}null(l)
Date html generated:
2019_06_20-PM-01_19_19
Last ObjectModification:
2018_09_30-PM-03_56_42
Theory : list_1
Home
Index