Nuprl Lemma : shorten-tuple-split-tuple
∀[n:ℕ]. ∀[x:Top]. (shorten-tuple(x;n) ~ snd(split-tuple(x;n)))
Proof
Definitions occuring in Statement :
shorten-tuple: shorten-tuple(x;n),
split-tuple: split-tuple(x;n),
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
pi2: snd(t),
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
all: ∀x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
shorten-tuple: shorten-tuple(x;n),
split-tuple: split-tuple(x;n),
le_int: i ≤z j,
lt_int: i <z j,
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
bfalse: ff,
subtract: n - m,
eq_int: (i =z j),
btrue: tt,
pi2: snd(t),
decidable: Dec(P),
or: P ∨ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
subtype_rel: A ⊆r B,
uiff: uiff(P;Q),
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
sq_type: SQType(T),
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
less_than_wf,
top_wf,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
le_int_wf,
bool_wf,
uiff_transitivity,
equal-wf-base,
int_subtype_base,
assert_wf,
le_wf,
eqtt_to_assert,
assert_of_le_int,
lt_int_wf,
bnot_wf,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_le_int,
assert_of_lt_int,
eq_int_wf,
assert_of_eq_int,
intformeq_wf,
int_formula_prop_eq_lemma,
iff_transitivity,
not_wf,
iff_weakening_uiff,
assert_of_bnot,
equal_wf,
nat_wf,
subtype_base_sq,
lifting-strict-spread,
strict4-spread
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
lambdaFormation,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
independent_functionElimination,
sqequalAxiom,
unionElimination,
equalityElimination,
because_Cache,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
equalityTransitivity,
equalitySymmetry,
productElimination,
impliesFunctionality,
instantiate,
cumulativity
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[x:Top]. (shorten-tuple(x;n) \msim{} snd(split-tuple(x;n)))
Date html generated:
2017_04_17-AM-09_29_58
Last ObjectModification:
2017_02_27-PM-05_30_34
Theory : tuples
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