Nuprl Lemma : sqequal-nil
∀[T:Type]. ∀[l:T List]. l ~ [] supposing l = [] ∈ (T List)
Proof
Definitions occuring in Statement :
nil: [],
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
sqequal: s ~ t,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
or: P ∨ Q,
cons: [a / b],
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
false: False,
uiff: uiff(P;Q),
top: Top,
prop: ℙ,
rev_implies: P ⇐ Q,
true: True,
not: ¬A
Lemmas referenced :
list-cases,
product_subtype_list,
iff_imp_equal_bool,
btrue_wf,
bfalse_wf,
assert_of_null,
null_cons_lemma,
istype-void,
true_wf,
false_wf,
btrue_neq_bfalse,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
hypothesisEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
dependent_functionElimination,
unionElimination,
promote_hyp,
hypothesis_subsumption,
productElimination,
sqequalRule,
independent_isectElimination,
independent_pairFormation,
Error :lambdaFormation_alt,
equalityTransitivity,
equalitySymmetry,
Error :isect_memberEquality_alt,
voidElimination,
Error :universeIsType,
natural_numberEquality,
independent_functionElimination,
axiomSqEquality,
Error :equalityIsType3,
Error :inhabitedIsType,
baseClosed,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[l:T List]. l \msim{} [] supposing l = []
Date html generated:
2019_06_20-PM-01_19_17
Last ObjectModification:
2018_09_30-PM-03_55_34
Theory : list_1
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