Nuprl Lemma : poss-maj-length
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[L:T List]. ∀[x:T]. ((fst(poss-maj(eq;L;x))) ≤ ||L||)
Proof
Definitions occuring in Statement :
poss-maj: poss-maj(eq;L;x),
length: ||as||,
list: T List,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
pi1: fst(t),
le: A ≤ B,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
poss-maj: poss-maj(eq;L;x),
all: ∀x:A. B[x],
implies: P ⇒ Q,
pi2: snd(t),
pi1: fst(t),
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T},
nat: ℕ,
false: False,
ge: i ≥ j ,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
le: A ≤ B,
or: P ∨ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
decidable: Dec(P),
cons: [a / b],
less_than': less_than'(a;b),
colength: colength(L),
nil: [],
it: ⋅,
so_lambda: λ2x.t[x],
so_apply: x[s],
less_than: a < b,
squash: ↓T,
subtype_rel: A ⊆r B,
deq: EqDecider(T),
bool: 𝔹,
unit: Unit,
btrue: tt,
uiff: uiff(P;Q),
eqof: eqof(d),
ifthenelse: if b then t else f fi ,
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
nequal: a ≠ b ∈ T
Lemmas referenced :
subtype_base_sq,
int_subtype_base,
add-zero,
length_wf,
nat_properties,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
istype-less_than,
le_witness_for_triv,
list-cases,
list_accum_nil_lemma,
length_of_nil_lemma,
decidable__le,
intformnot_wf,
itermAdd_wf,
int_formula_prop_not_lemma,
int_term_value_add_lemma,
product_subtype_list,
colength-cons-not-zero,
colength_wf_list,
istype-false,
istype-le,
subtract-1-ge-0,
intformeq_wf,
int_formula_prop_eq_lemma,
set_subtype_base,
spread_cons_lemma,
decidable__equal_int,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
le_wf,
list_accum_cons_lemma,
length_of_cons_lemma,
eqtt_to_assert,
safe-assert-deq,
eqff_to_assert,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
iff_weakening_uiff,
assert_wf,
equal_wf,
eq_int_wf,
assert_of_eq_int,
neg_assert_of_eq_int,
istype-nat,
list_wf,
deq_wf,
istype-universe,
list_accum_wf,
ifthenelse_wf,
add-is-int-iff,
false_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
independent_pairEquality,
natural_numberEquality,
hypothesisEquality,
Error :inhabitedIsType,
hypothesis,
Error :lambdaFormation_alt,
thin,
productElimination,
applyLambdaEquality,
sqequalRule,
sqequalHypSubstitution,
instantiate,
extract_by_obid,
isectElimination,
cumulativity,
intEquality,
independent_isectElimination,
equalitySymmetry,
dependent_functionElimination,
equalityTransitivity,
independent_functionElimination,
setElimination,
rename,
intWeakElimination,
approximateComputation,
Error :dependent_pairFormation_alt,
Error :lambdaEquality_alt,
int_eqEquality,
Error :isect_memberEquality_alt,
voidElimination,
independent_pairFormation,
Error :universeIsType,
Error :functionIsTypeImplies,
unionElimination,
addEquality,
promote_hyp,
hypothesis_subsumption,
Error :equalityIstype,
because_Cache,
Error :dependent_set_memberEquality_alt,
imageElimination,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
sqequalBase,
equalityElimination,
Error :isectIsTypeImplies,
universeEquality,
productEquality,
Error :productIsType,
pointwiseFunctionality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[L:T List]. \mforall{}[x:T]. ((fst(poss-maj(eq;L;x))) \mleq{} ||L||)
Date html generated:
2019_06_20-PM-01_54_42
Last ObjectModification:
2018_11_28-PM-05_14_41
Theory : decidable!equality
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