Nuprl Lemma : sq-decider-list-deq
∀[eq:Base]. sq-decider(list-deq(eq)) supposing sq-decider(eq)
Proof
Definitions occuring in Statement :
list-deq: list-deq(eq),
sq-decider: sq-decider(eq),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
base: Base
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
sq-decider: sq-decider(eq),
implies: P ⇒ Q,
exists: ∃x:A. B[x],
list-deq: list-deq(eq),
list_ind: list_ind,
nat: ℕ,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
all: ∀x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
decidable: Dec(P),
or: P ∨ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
nat_plus: ℕ+,
has-value: (a)↓,
band: p ∧b q,
bfalse: ff,
ifthenelse: if b then t else f fi ,
outl: outl(x),
cand: A c∧ B,
sq_type: SQType(T),
guard: {T},
true: True,
null: null(as),
btrue: tt
Lemmas referenced :
value-type-has-value,
base_wf,
union-value-type,
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
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,
less_than_wf,
has-value_wf_base,
int_subtype_base,
fun_exp0_lemma,
strictness-apply,
bottom_diverge,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
exists_wf,
sqequal-wf-base,
sq-decider_wf,
fun_exp_unroll_1,
has-value-implies-dec-ispair-2,
top_wf,
equal_wf,
subtype_base_sq,
has-value-implies-dec-isaxiom-2,
subtype_rel_self
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
hypothesis,
extract_by_obid,
isectElimination,
unionEquality,
voidEquality,
independent_isectElimination,
inlEquality,
hypothesisEquality,
compactness,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
independent_pairFormation,
computeAll,
independent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
sqequalIntensionalEquality,
baseApply,
closedConclusion,
baseClosed,
because_Cache,
applyEquality,
unionElimination,
sqequalAxiom,
dependent_set_memberEquality,
callbyvalueApply,
callbyvalueCallbyvalue,
callbyvalueReduce,
callbyvalueDecide,
instantiate,
cumulativity,
promote_hyp,
addLevel,
levelHypothesis,
callbyvalueIspair
Latex:
\mforall{}[eq:Base]. sq-decider(list-deq(eq)) supposing sq-decider(eq)
Date html generated:
2017_09_29-PM-06_04_19
Last ObjectModification:
2017_07_26-PM-02_53_03
Theory : decidable!equality
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