Nuprl Lemma : poss-maj-member
∀T:Type. ∀eq:EqDecider(T). ∀L:T List. ∀x:T. (snd(poss-maj(eq;L;x)) ∈ [x / L])
Proof
Definitions occuring in Statement :
poss-maj: poss-maj(eq;L;x),
l_member: (x ∈ l),
cons: [a / b],
list: T List,
deq: EqDecider(T),
pi2: snd(t),
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
poss-maj: poss-maj(eq;L;x),
so_lambda: λ2x.t[x],
so_lambda: λ2x y.t[x; y],
deq: EqDecider(T),
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
eqof: eqof(d),
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
le: A ≤ B,
less_than': less_than'(a;b),
int_upper: {i...},
so_apply: x[s1;s2],
so_apply: x[s],
pi2: snd(t),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
gt: i > j
Lemmas referenced :
list_wf,
deq_wf,
list_induction,
all_wf,
nat_wf,
l_member_wf,
list_accum_wf,
bool_wf,
eqtt_to_assert,
safe-assert-deq,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermAdd_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_add_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
le_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
eq_int_wf,
assert_of_eq_int,
false_wf,
neg_assert_of_eq_int,
int_upper_subtype_nat,
nequal-le-implies,
zero-add,
subtract_wf,
int_upper_properties,
itermSubtract_wf,
int_term_value_subtract_lemma,
pi2_wf,
cons_wf,
list_accum_nil_lemma,
cons_member,
nil_wf,
list_accum_cons_lemma,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
eqof_wf,
uiff_transitivity,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
ifthenelse_wf,
decidable__lt,
intformless_wf,
intformeq_wf,
int_formula_prop_less_lemma,
int_formula_prop_eq_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
hypothesisEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesis,
universeEquality,
sqequalRule,
lambdaEquality,
because_Cache,
productElimination,
applyEquality,
setElimination,
rename,
unionElimination,
equalityElimination,
independent_isectElimination,
independent_pairEquality,
dependent_set_memberEquality,
addEquality,
natural_numberEquality,
dependent_functionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
equalityTransitivity,
equalitySymmetry,
promote_hyp,
instantiate,
independent_functionElimination,
hypothesis_subsumption,
productEquality,
inlFormation,
baseClosed,
addLevel,
impliesFunctionality,
levelHypothesis,
spreadEquality,
inrFormation,
hyp_replacement,
applyLambdaEquality
Latex:
\mforall{}T:Type. \mforall{}eq:EqDecider(T). \mforall{}L:T List. \mforall{}x:T. (snd(poss-maj(eq;L;x)) \mmember{} [x / L])
Date html generated:
2017_04_17-AM-09_08_45
Last ObjectModification:
2017_02_27-PM-05_17_35
Theory : decidable!equality
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