Nuprl Lemma : sorted-by-nil
∀[R:Top]. uiff(sorted-by(R;[]);True)
Proof
Definitions occuring in Statement :
sorted-by: sorted-by(R;L),
nil: [],
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
top: Top,
true: True
Definitions unfolded in proof :
sorted-by: sorted-by(R;L),
uall: ∀[x:A]. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
true: True,
prop: ℙ,
so_lambda: λ2x.t[x],
int_seg: {i..j-},
select: L[n],
all: ∀x:A. B[x],
nil: [],
it: ⋅,
so_lambda: λ2x y.t[x; y],
top: Top,
so_apply: x[s1;s2],
guard: {T},
lelt: i ≤ j < k,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
so_apply: x[s]
Lemmas referenced :
top_wf,
true_wf,
int_formula_prop_wf,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_and_lemma,
itermConstant_wf,
intformle_wf,
itermVar_wf,
intformless_wf,
intformand_wf,
satisfiable-full-omega-tt,
int_seg_properties,
base_wf,
stuck-spread,
length_of_nil_lemma,
nil_wf,
length_wf,
int_seg_wf,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
independent_pairFormation,
introduction,
cut,
natural_numberEquality,
sqequalHypSubstitution,
axiomEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
lemma_by_obid,
isectElimination,
thin,
voidEquality,
because_Cache,
lambdaEquality,
setElimination,
rename,
hypothesisEquality,
baseClosed,
independent_isectElimination,
lambdaFormation,
isect_memberEquality,
voidElimination,
productElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
dependent_functionElimination,
computeAll
Latex:
\mforall{}[R:Top]. uiff(sorted-by(R;[]);True)
Date html generated:
2016_05_14-PM-01_46_55
Last ObjectModification:
2016_01_15-AM-08_19_30
Theory : list_1
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