Nuprl Lemma : no_repeats-subtype
∀[T,S:Type]. ∀[L:S List]. no_repeats(S;L) supposing no_repeats(T;L) supposing S ⊆r T
Proof
Definitions occuring in Statement :
no_repeats: no_repeats(T;l),
list: T List,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
no_repeats: no_repeats(T;l),
not: ¬A,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
prop: ℙ,
false: False,
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],
top: Top,
and: P ∧ Q
Lemmas referenced :
equal_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,
not_wf,
nat_wf,
less_than_wf,
length_wf,
no_repeats_witness,
no_repeats_wf,
subtype_rel_list,
list_wf,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
lambdaFormation,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
applyEquality,
sqequalRule,
hyp_replacement,
applyLambdaEquality,
extract_by_obid,
cumulativity,
because_Cache,
voidElimination,
setElimination,
rename,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidEquality,
independent_pairFormation,
computeAll,
universeEquality
Latex:
\mforall{}[T,S:Type]. \mforall{}[L:S List]. no\_repeats(S;L) supposing no\_repeats(T;L) supposing S \msubseteq{}r T
Date html generated:
2017_04_17-AM-07_29_01
Last ObjectModification:
2017_02_27-PM-04_06_37
Theory : list_1
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