Nuprl Lemma : list-cases
∀[T:Type]. ∀x:T List. ((x ~ []) ∨ (x ∈ T × (T List)))
Proof
Definitions occuring in Statement :
nil: [],
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
or: P ∨ Q,
member: t ∈ T,
product: x:A × B[x],
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
list: T List,
or: P ∨ Q,
it: ⋅,
nil: [],
top: Top,
uimplies: b supposing a,
so_apply: x[s],
so_lambda: λ2x.t[x],
guard: {T},
subtype_rel: A ⊆r B,
pi1: fst(t),
pi2: snd(t),
prop: ℙ,
nat: ℕ,
and: P ∧ Q,
has-value: (a)↓,
implies: P ⇒ Q,
colength: colength(L)
Lemmas referenced :
list_wf,
istype-universe,
colist-cases,
istype-void,
istype-top,
top_wf,
colist_wf,
subtype_rel_product,
pair-eta,
colength_wf,
int-value-type,
istype-int,
le_wf,
set-value-type,
nat_wf,
has-value_wf-partial,
value-type-has-value,
int_subtype_base,
set_subtype_base,
subtype_partial_sqtype_base,
pair-sq-axiom-wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
Error :lambdaFormation_alt,
Error :universeIsType,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
instantiate,
universeEquality,
setElimination,
rename,
dependent_functionElimination,
unionElimination,
sqequalRule,
because_Cache,
baseClosed,
Error :productIsType,
Error :equalityIsType4,
Error :inlFormation_alt,
Error :inrFormation_alt,
voidElimination,
Error :isect_memberEquality_alt,
independent_isectElimination,
cumulativity,
Error :lambdaEquality_alt,
applyEquality,
equalitySymmetry,
equalityTransitivity,
productElimination,
applyLambdaEquality,
independent_pairEquality,
natural_numberEquality,
intEquality,
Error :dependent_set_memberEquality_alt,
callbyvalueAdd,
independent_functionElimination,
Error :inhabitedIsType,
Error :equalityIsType1
Latex:
\mforall{}[T:Type]. \mforall{}x:T List. ((x \msim{} []) \mvee{} (x \mmember{} T \mtimes{} (T List)))
Date html generated:
2019_06_20-PM-00_38_36
Last ObjectModification:
2018_10_18-PM-01_28_03
Theory : list_0
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