Nuprl Lemma : no_repeats_safety
∀[A:Type]. safety(A;L.no_repeats(A;L))
Proof
Definitions occuring in Statement :
safety: safety(A;tr.P[tr]),
no_repeats: no_repeats(T;l),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
no_repeats: no_repeats(T;l),
safety: safety(A;tr.P[tr]),
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
uimplies: b supposing a,
not: ¬A,
false: False,
prop: ℙ,
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
and: P ∧ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
cand: A c∧ B,
le: A ≤ B
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,
uall_wf,
isect_wf,
iseg_wf,
list_wf,
iseg_length,
iseg_select,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
hypothesis,
sqequalHypSubstitution,
independent_functionElimination,
voidElimination,
extract_by_obid,
isectElimination,
cumulativity,
hypothesisEquality,
because_Cache,
setElimination,
rename,
independent_isectElimination,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidEquality,
independent_pairFormation,
computeAll,
equalityTransitivity,
equalitySymmetry,
universeEquality,
productElimination,
hyp_replacement,
applyLambdaEquality
Latex:
\mforall{}[A:Type]. safety(A;L.no\_repeats(A;L))
Date html generated:
2017_10_01-AM-08_34_18
Last ObjectModification:
2017_07_26-PM-04_25_27
Theory : list!
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