Nuprl Lemma : select_equal
∀[T:Type]. ∀[a,b:T List]. ∀[i:ℕ]. (a[i] = b[i] ∈ T) supposing (i < ||a|| and (a = b ∈ (T List)))
Proof
Definitions occuring in Statement :
select: L[n],
length: ||as||,
list: T List,
nat: ℕ,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat: ℕ,
uimplies: b supposing a,
prop: ℙ,
implies: P ⇒ Q,
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,
not: ¬A,
top: Top,
and: P ∧ Q
Lemmas referenced :
less_than_wf,
length_wf,
equal_wf,
list_wf,
nat_wf,
select_wf,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
cumulativity,
because_Cache,
universeEquality,
isect_memberFormation,
sqequalRule,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
hyp_replacement,
applyLambdaEquality,
lambdaFormation,
independent_isectElimination,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
functionEquality,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[a,b:T List]. \mforall{}[i:\mBbbN{}]. (a[i] = b[i]) supposing (i < ||a|| and (a = b))
Date html generated:
2017_04_17-AM-08_42_56
Last ObjectModification:
2017_02_27-PM-05_01_50
Theory : list_1
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