Nuprl Lemma : cons_neq_nil
∀[T:Type]. ∀[h:T]. ∀[t:T List]. (¬([h / t] = [] ∈ (T List)))
Proof
Definitions occuring in Statement :
cons: [a / b],
nil: [],
list: T List,
uall: ∀[x:A]. B[x],
not: ¬A,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
not: ¬A,
implies: P ⇒ Q,
false: False,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
all: ∀x:A. B[x],
top: Top,
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T},
true: True
Lemmas referenced :
equal-wf-T-base,
list_wf,
cons_wf,
list_ind_wf,
list_ind_cons_lemma,
list_ind_nil_lemma,
subtype_base_sq,
int_subtype_base
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
baseClosed,
because_Cache,
Error :universeIsType,
universeEquality,
sqequalRule,
Error :isect_memberFormation_alt,
lambdaFormation,
lambdaEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
applyLambdaEquality,
intEquality,
natural_numberEquality,
voidEquality,
instantiate,
cumulativity,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[h:T]. \mforall{}[t:T List]. (\mneg{}([h / t] = []))
Date html generated:
2019_06_20-PM-00_38_46
Last ObjectModification:
2018_09_26-PM-02_07_28
Theory : list_0
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