Nuprl Lemma : assert-palindrome-test
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[L:T List]. uiff(↑palindrome-test(eq;L);rev(L) = L ∈ (T List))
Proof
Definitions occuring in Statement :
palindrome-test: palindrome-test(eq;L),
reverse: rev(as),
list: T List,
deq: EqDecider(T),
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
palindrome-test: palindrome-test(eq;L),
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
has-value: (a)↓,
bool: 𝔹,
deq: EqDecider(T),
so_apply: x[s1;s2;s3],
all: ∀x:A. B[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
implies: P ⇒ Q,
guard: {T},
iff: P ⇐⇒ Q,
subtype_rel: A ⊆r B,
prop: ℙ,
rev_implies: P ⇐ Q,
top: Top,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
btrue: tt,
nat: ℕ,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
or: P ∨ Q,
assert: ↑b,
list-deq: list-deq(eq),
list_ind: list_ind,
nil: [],
it: ⋅,
null: null(as),
true: True,
sq_type: SQType(T),
cons: [a / b],
colength: colength(L),
so_lambda: λ2x.t[x],
so_apply: x[s],
le: A ≤ B,
decidable: Dec(P),
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
unit: Unit,
bfalse: ff,
bnot: ¬bb,
eqof: eqof(d)
Lemmas referenced :
iff_weakening_uiff,
assert_wf,
taba_wf,
bool_wf,
btrue_wf,
value-type-has-value,
union-value-type,
unit_wf2,
band_wf,
list_accum_wf,
zip_wf,
reverse_wf,
assert_functionality_wrt_uiff,
taba-property,
assert_witness,
equal_wf,
list_wf,
uiff_wf,
palindrome-test_wf,
deq_wf,
length-reverse,
length_wf,
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,
equal-wf-T-base,
nat_wf,
colength_wf_list,
less_than_transitivity1,
less_than_irreflexivity,
list-cases,
length_of_nil_lemma,
zip_nil_lemma,
list_accum_nil_lemma,
subtype_base_sq,
bool_subtype_base,
iff_imp_equal_bool,
list-deq_wf,
nil_wf,
assert_of_band,
iff_wf,
equal-wf-base,
product_subtype_list,
spread_cons_lemma,
set_subtype_base,
le_wf,
int_subtype_base,
length_of_cons_lemma,
zip_cons_nil_lemma,
cons_wf,
non_neg_length,
intformeq_wf,
itermAdd_wf,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
decidable__le,
intformnot_wf,
int_formula_prop_not_lemma,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
decidable__equal_int,
equal-wf-base-T,
zip_cons_cons_lemma,
list_accum_cons_lemma,
add-is-int-iff,
false_wf,
eqtt_to_assert,
eqff_to_assert,
bool_cases_sqequal,
assert-bnot,
bfalse_wf,
eqof_wf,
iff_transitivity,
safe-assert-deq,
reduce_hd_cons_lemma,
hd_wf,
squash_wf,
length_cons_ge_one,
subtype_rel_list,
top_wf,
reduce_tl_cons_lemma,
and_wf,
tl_wf,
deq_property
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
addLevel,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairFormation,
isect_memberFormation,
independent_isectElimination,
introduction,
extract_by_obid,
isectElimination,
cumulativity,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality,
callbyvalueReduce,
because_Cache,
applyEquality,
setElimination,
rename,
dependent_functionElimination,
productEquality,
independent_functionElimination,
universeEquality,
independent_pairEquality,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lambdaFormation,
voidElimination,
voidEquality,
hyp_replacement,
applyLambdaEquality,
intEquality,
intWeakElimination,
natural_numberEquality,
dependent_pairFormation,
int_eqEquality,
computeAll,
sqequalAxiom,
unionElimination,
baseClosed,
instantiate,
impliesFunctionality,
promote_hyp,
hypothesis_subsumption,
addEquality,
dependent_set_memberEquality,
imageElimination,
pointwiseFunctionality,
baseApply,
closedConclusion,
equalityElimination,
levelHypothesis,
andLevelFunctionality,
impliesLevelFunctionality,
imageMemberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[L:T List]. uiff(\muparrow{}palindrome-test(eq;L);rev(L) = L)
Date html generated:
2018_05_21-PM-09_01_34
Last ObjectModification:
2017_07_26-PM-06_24_32
Theory : general
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