Nuprl Lemma : poss-maj-property
∀T:Type. ∀eq:EqDecider(T). ∀L:T List. ∀x:T. possible-majority(T;eq;L;snd(poss-maj(eq;L;x)))
Proof
Definitions occuring in Statement :
poss-maj: poss-maj(eq;L;x),
possible-majority: possible-majority(T;eq;L;x),
list: T List,
deq: EqDecider(T),
pi2: snd(t),
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
prop: ℙ,
pi2: snd(t),
implies: P ⇒ Q,
so_apply: x[s],
so_lambda: λ2x.t[x],
nat: ℕ,
subtype_rel: A ⊆r B,
or: P ∨ Q,
decidable: Dec(P),
deq: EqDecider(T),
possible-majority: possible-majority(T;eq;L;x),
and: P ∧ Q,
uimplies: b supposing a,
uiff: uiff(P;Q),
istype: istype(T),
ge: i ≥ j ,
false: False,
le: A ≤ B,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top
Lemmas referenced :
deq_wf,
list_wf,
poss-maj-invariant,
equal_wf,
nat_wf,
poss-maj_wf,
assert_wf,
not_wf,
all_wf,
bnot_wf,
subtract_wf,
le_wf,
count_wf,
length_wf,
less_than_wf,
decidable__assert,
deq_property2,
count-length-filter,
filter-split-length,
filter_functionality,
eta_conv,
bool_wf,
filter_wf5,
subtype_rel_dep_function,
l_member_wf,
nat_properties,
subtract-is-int-iff,
full-omega-unsat,
intformand_wf,
intformeq_wf,
itermVar_wf,
itermAdd_wf,
intformle_wf,
itermSubtract_wf,
intformless_wf,
itermMultiply_wf,
itermConstant_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_formula_prop_le_lemma,
int_term_value_subtract_lemma,
int_formula_prop_less_lemma,
int_term_value_mul_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
false_wf
Rules used in proof :
universeEquality,
isectElimination,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
hypothesis,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
extract_by_obid,
introduction,
cut,
independent_functionElimination,
equalitySymmetry,
equalityTransitivity,
sqequalRule,
rename,
productElimination,
productEquality,
cumulativity,
functionEquality,
lambdaEquality,
natural_numberEquality,
multiplyEquality,
unionElimination,
because_Cache,
setElimination,
applyEquality,
independent_isectElimination,
independent_pairFormation,
Error :lambdaEquality_alt,
Error :inhabitedIsType,
setEquality,
Error :setIsType,
Error :universeIsType,
Error :lambdaFormation_alt,
pointwiseFunctionality,
promote_hyp,
baseApply,
closedConclusion,
baseClosed,
approximateComputation,
Error :dependent_pairFormation_alt,
int_eqEquality,
Error :isect_memberEquality_alt,
voidElimination
Latex:
\mforall{}T:Type. \mforall{}eq:EqDecider(T). \mforall{}L:T List. \mforall{}x:T. possible-majority(T;eq;L;snd(poss-maj(eq;L;x)))
Date html generated:
2019_06_20-PM-01_54_39
Last ObjectModification:
2019_01_17-AM-09_49_21
Theory : decidable!equality
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