Nuprl Lemma : nth_tl_nth_tl
∀[m,n:ℕ]. ∀[L:Top List]. (nth_tl(m;nth_tl(n;L)) ~ nth_tl(m + n;L))
Proof
Definitions occuring in Statement :
nth_tl: nth_tl(n;as),
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
add: n + m,
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,
nth_tl: nth_tl(n;as),
le_int: i ≤z j,
lt_int: i <z j,
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
decidable: Dec(P),
or: P ∨ Q,
subtype_rel: A ⊆r B,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
guard: {T}
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,
list_wf,
top_wf,
nat_wf,
zero-add,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
le_int_wf,
bool_wf,
equal-wf-base,
int_subtype_base,
assert_wf,
le_wf,
lt_int_wf,
bnot_wf,
equal-wf-T-base,
itermAdd_wf,
int_term_value_add_lemma,
uiff_transitivity,
eqtt_to_assert,
assert_of_le_int,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_le_int,
assert_of_lt_int,
equal_wf,
tl_wf,
general_arith_equation1
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,
because_Cache,
unionElimination,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
addEquality,
equalityElimination,
productElimination,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[m,n:\mBbbN{}]. \mforall{}[L:Top List]. (nth\_tl(m;nth\_tl(n;L)) \msim{} nth\_tl(m + n;L))
Date html generated:
2017_04_14-AM-09_26_08
Last ObjectModification:
2017_02_27-PM-04_00_18
Theory : list_1
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