Nuprl Lemma : test_case1_wf
test_case1() ∈ ℚ List + Atom
Proof
Definitions occuring in Statement :
test_case1: test_case1(),
rationals: ℚ,
list: T List,
member: t ∈ T,
union: left + right,
atom: Atom
Definitions unfolded in proof :
test_case1: test_case1(),
member: t ∈ T,
subtype_rel: A ⊆r B,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
uimplies: b supposing a,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
length: ||as||,
list_ind: list_ind,
cons: [a / b],
nil: [],
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_exists: ∃x:A [B[x]]
Lemmas referenced :
decidable__q-constraints,
false_wf,
le_wf,
cons_wf,
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
select_wf,
nil_wf,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_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_var_lemma,
int_formula_prop_wf,
int-subtype-rationals,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
less_than_wf,
decidable_wf,
sq_exists_wf,
list_wf,
rationals_wf,
q-constraints_wf,
nat_wf,
not_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
applyEquality,
instantiate,
extract_by_obid,
hypothesis,
thin,
because_Cache,
sqequalHypSubstitution,
sqequalRule,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
introduction,
isectElimination,
hypothesisEquality,
independent_pairEquality,
lambdaEquality,
setElimination,
rename,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
intEquality,
dependent_functionElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
equalityTransitivity,
equalitySymmetry,
promote_hyp,
cumulativity,
productEquality,
functionEquality,
unionEquality,
inlEquality,
atomEquality,
inrEquality,
tokenEquality
Latex:
test\_case1() \mmember{} \mBbbQ{} List + Atom
Date html generated:
2019_10_16-PM-00_37_10
Last ObjectModification:
2018_08_21-PM-02_00_17
Theory : rationals
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