Nuprl Lemma : reject_cons_tl_sq
∀[T:Type]. ∀[a:T]. ∀[as:T List]. ∀[i:ℤ]. ([a / as]\[i] ~ [a / as\[i - 1]]) supposing ((i ≤ ||as||) and 0 < i)
Proof
Definitions occuring in Statement :
length: ||as||,
reject: as\[i],
cons: [a / b],
list: T List,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
subtract: n - m,
natural_number: $n,
int: ℤ,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
reject: as\[i],
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
top: Top,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
prop: ℙ,
bfalse: ff,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3]
Lemmas referenced :
le_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_le_int,
reduce_tl_cons_lemma,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermVar_wf,
itermConstant_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
le_wf,
list_ind_cons_lemma,
length_wf,
less_than_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
natural_numberEquality,
hypothesis,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
independent_pairFormation,
computeAll,
promote_hyp,
instantiate,
cumulativity,
independent_functionElimination,
because_Cache,
sqequalAxiom,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[a:T]. \mforall{}[as:T List]. \mforall{}[i:\mBbbZ{}].
([a / as]\mbackslash{}[i] \msim{} [a / as\mbackslash{}[i - 1]]) supposing ((i \mleq{} ||as||) and 0 < i)
Date html generated:
2017_04_17-AM-08_48_39
Last ObjectModification:
2017_02_27-PM-05_05_59
Theory : list_1
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