Nuprl Lemma : shorten-tuple_wf2
∀[L1,L2:Type List]. ∀[x:tuple-type(L1 @ L2)]. shorten-tuple(x;||L1||) ∈ tuple-type(L2) supposing 0 < ||L2||
Proof
Definitions occuring in Statement :
shorten-tuple: shorten-tuple(x;n),
tuple-type: tuple-type(L),
length: ||as||,
append: as @ bs,
list: T List,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
less_than: a < b,
squash: ↓T,
subtype_rel: A ⊆r B,
guard: {T},
int_iseg: {i...j},
cand: A c∧ B
Lemmas referenced :
list_wf,
tuple-type_wf,
less_than_wf,
int_seg_wf,
top_wf,
subtype_rel_list,
int_term_value_subtract_lemma,
int_formula_prop_eq_lemma,
itermSubtract_wf,
intformeq_wf,
le_wf,
and_wf,
length_nth_tl,
length_append,
int_seg_properties,
select_wf,
subtype_rel-equal,
nth_tl_append,
nth_tl_wf,
subtype_rel_tuple-type,
lelt_wf,
int_term_value_add_lemma,
int_formula_prop_less_lemma,
itermAdd_wf,
intformless_wf,
length_wf,
decidable__lt,
length-append,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
non_neg_length,
append_wf,
shorten-tuple_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
instantiate,
universeEquality,
hypothesisEquality,
hypothesis,
dependent_set_memberEquality,
because_Cache,
independent_pairFormation,
dependent_functionElimination,
unionElimination,
productElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
computeAll,
addEquality,
imageElimination,
applyEquality,
lambdaFormation,
setElimination,
rename,
equalityTransitivity,
equalitySymmetry,
cumulativity,
axiomEquality
Latex:
\mforall{}[L1,L2:Type List]. \mforall{}[x:tuple-type(L1 @ L2)].
shorten-tuple(x;||L1||) \mmember{} tuple-type(L2) supposing 0 < ||L2||
Date html generated:
2016_05_14-PM-03_58_38
Last ObjectModification:
2016_01_14-PM-10_35_28
Theory : tuples
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