Nuprl Lemma : default-partition-choice_wf
∀[p:ℝ List]. default-partition-choice(p) ∈ partition-choice(p) supposing frs-non-dec(p)
Proof
Definitions occuring in Statement :
default-partition-choice: default-partition-choice(p),
partition-choice: partition-choice(p),
frs-non-dec: frs-non-dec(L),
real: ℝ,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
subtract: n - m,
le: A ≤ B,
frs-non-dec: frs-non-dec(L),
cand: A c∧ B,
uiff: uiff(P;Q),
squash: ↓T,
less_than: a < b,
prop: ℙ,
not: ¬A,
implies: P ⇒ Q,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
or: P ∨ Q,
decidable: Dec(P),
and: P ∧ Q,
lelt: i ≤ j < k,
guard: {T},
int_seg: {i..j-},
top: Top,
all: ∀x:A. B[x],
partition-choice: partition-choice(p),
default-partition-choice: default-partition-choice(p),
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
member_rccint_lemma,
select_wf,
real_wf,
int_seg_properties,
subtract_wf,
length_wf,
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,
decidable__lt,
subtract-is-int-iff,
intformless_wf,
itermSubtract_wf,
int_formula_prop_less_lemma,
int_term_value_subtract_lemma,
false_wf,
rleq_weakening_equal,
lelt_wf,
add-member-int_seg2,
itermAdd_wf,
int_term_value_add_lemma,
rleq_wf,
int_seg_wf,
frs-non-dec_wf,
list_wf
Rules used in proof :
axiomEquality,
productEquality,
addEquality,
independent_functionElimination,
baseClosed,
closedConclusion,
baseApply,
imageElimination,
promote_hyp,
equalitySymmetry,
equalityTransitivity,
pointwiseFunctionality,
because_Cache,
computeAll,
independent_pairFormation,
intEquality,
int_eqEquality,
dependent_pairFormation,
unionElimination,
productElimination,
natural_numberEquality,
independent_isectElimination,
rename,
setElimination,
hypothesisEquality,
isectElimination,
dependent_set_memberEquality,
lambdaEquality,
hypothesis,
voidEquality,
voidElimination,
isect_memberEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
lemma_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[p:\mBbbR{} List]. default-partition-choice(p) \mmember{} partition-choice(p) supposing frs-non-dec(p)
Date html generated:
2016_05_18-AM-10_39_16
Last ObjectModification:
2016_01_17-AM-00_21_44
Theory : reals
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