Nuprl Lemma : sorted-by-single
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. ∀x:T. sorted-by(R;[x])
Proof
Definitions occuring in Statement :
sorted-by: sorted-by(R;L),
cons: [a / b],
nil: [],
uall: ∀[x:A]. B[x],
prop: ℙ,
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
sorted-by: sorted-by(R;L),
member: t ∈ T,
top: Top,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
prop: ℙ
Lemmas referenced :
int_seg_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,
length_of_nil_lemma,
length_of_cons_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
sqequalRule,
cut,
lemma_by_obid,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isectElimination,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
productElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
independent_pairFormation,
computeAll,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. \mforall{}x:T. sorted-by(R;[x])
Date html generated:
2016_05_14-PM-01_47_18
Last ObjectModification:
2016_01_15-AM-08_18_48
Theory : list_1
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