Nuprl Lemma : nth_tl_decomp_eq
∀[T:Type]. ∀[m:ℕ]. ∀[L:T List]. nth_tl(m;L) = [L[m] / nth_tl(1 + m;L)] ∈ (T List) supposing m < ||L||
Proof
Definitions occuring in Statement :
select: L[n],
length: ||as||,
nth_tl: nth_tl(n;as),
cons: [a / b],
list: T List,
nat: ℕ,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
add: n + m,
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
nat: ℕ,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
nat_wf,
list_wf,
length_wf,
less_than_wf,
nth_tl_wf,
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,
nat_properties,
select_wf,
cons_wf,
nth_tl_decomp
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
cumulativity,
because_Cache,
setElimination,
rename,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
addEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[m:\mBbbN{}]. \mforall{}[L:T List]. nth\_tl(m;L) = [L[m] / nth\_tl(1 + m;L)] supposing m < ||L||
Date html generated:
2016_05_14-AM-07_37_23
Last ObjectModification:
2016_01_15-AM-08_43_35
Theory : list_1
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