Nuprl Lemma : no_repeats-strong-subtype
∀[T,S:Type]. ∀[L:S List]. (no_repeats(T;L)) supposing (no_repeats(S;L) and strong-subtype(S;T))
Proof
Definitions occuring in Statement :
no_repeats: no_repeats(T;l),
list: T List,
strong-subtype: strong-subtype(A;B),
uimplies: b supposing a,
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,
guard: {T},
label: ...$L... t,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
strong-subtype: strong-subtype(A;B),
cand: A c∧ B,
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
strong-subtype-implies,
select_wf,
subtype_rel_list,
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,
equal_wf,
not_wf,
nat_wf,
less_than_wf,
length_wf,
no_repeats_witness,
no_repeats_wf,
strong-subtype_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
lambdaFormation,
independent_functionElimination,
extract_by_obid,
dependent_functionElimination,
cumulativity,
applyEquality,
productElimination,
sqequalRule,
setElimination,
rename,
because_Cache,
natural_numberEquality,
unionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
addLevel,
levelHypothesis,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T,S:Type]. \mforall{}[L:S List]. (no\_repeats(T;L)) supposing (no\_repeats(S;L) and strong-subtype(S;T))
Date html generated:
2017_04_17-AM-07_29_06
Last ObjectModification:
2017_02_27-PM-04_07_40
Theory : list_1
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