Nuprl Lemma : tuple-type-valueall-type
∀[L:{T:Type| valueall-type(T)} List]. valueall-type(tuple-type(L))
Proof
Definitions occuring in Statement :
tuple-type: tuple-type(L),
list: T List,
valueall-type: valueall-type(T),
uall: ∀[x:A]. B[x],
set: {x:A| B[x]} ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
prop: ℙ,
subtype_rel: A ⊆r B,
so_apply: x[s],
implies: P ⇒ Q,
unit: Unit,
all: ∀x:A. B[x],
top: Top,
bool: 𝔹,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
sq_stable: SqStable(P),
squash: ↓T,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
valueall-type: valueall-type(T),
has-value: (a)↓
Lemmas referenced :
list_induction,
valueall-type_wf,
tuple-type_wf,
list_wf,
tupletype_nil_lemma,
equal-valueall-type,
tupletype_cons_lemma,
null_wf,
bool_wf,
eqtt_to_assert,
assert_of_null,
sq_stable__valueall-type,
equal_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
equal-wf-T-base,
product-valueall-type,
equal-wf-base,
subtype_rel_list,
base_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
because_Cache,
sqequalRule,
lambdaEquality,
cumulativity,
hypothesisEquality,
applyEquality,
hypothesis,
setEquality,
universeEquality,
independent_functionElimination,
intEquality,
natural_numberEquality,
lambdaFormation,
rename,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
setElimination,
imageMemberEquality,
baseClosed,
imageElimination,
equalityTransitivity,
equalitySymmetry,
dependent_pairFormation,
promote_hyp,
axiomSqleEquality
Latex:
\mforall{}[L:\{T:Type| valueall-type(T)\} List]. valueall-type(tuple-type(L))
Date html generated:
2017_04_17-AM-09_29_03
Last ObjectModification:
2017_02_27-PM-05_29_03
Theory : tuples
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