Nuprl Lemma : is-list-if-has-value-fun-ax-mem
∀[t:Base]. ∀[n:ℕ]. Ax ∈ is-list-if-has-value-fun(t;n) supposing is-list-if-has-value-fun(t;n)
Proof
Definitions occuring in Statement :
is-list-if-has-value-fun: is-list-if-has-value-fun(t;n),
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
base: Base,
axiom: Ax
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
all: ∀x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
is-list-if-has-value-fun: is-list-if-has-value-fun(t;n),
unit: Unit,
decidable: Dec(P),
or: P ∨ Q,
exposed-it: exposed-it,
bool: 𝔹,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
nequal: a ≠ b ∈ T ,
subtype_rel: A ⊆r B,
has-value: (a)↓,
pi2: snd(t),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
true: True
Lemmas referenced :
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,
is-list-if-has-value-fun_wf,
base_wf,
primrec0_lemma,
unit_wf2,
le_wf,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
primrec-unroll,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
intformeq_wf,
int_formula_prop_eq_lemma,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
nat_wf,
assert_wf,
bnot_wf,
not_wf,
equal-wf-base,
int_subtype_base,
has-value-implies-dec-ispair-2,
has-value_wf_base,
bool_cases,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
isaxiom-implies
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
sqequalRule,
intWeakElimination,
lambdaFormation,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
dependent_set_memberEquality,
unionElimination,
because_Cache,
equalityElimination,
productElimination,
promote_hyp,
instantiate,
cumulativity,
applyEquality,
baseClosed,
baseApply,
closedConclusion,
impliesFunctionality
Latex:
\mforall{}[t:Base]. \mforall{}[n:\mBbbN{}]. Ax \mmember{} is-list-if-has-value-fun(t;n) supposing is-list-if-has-value-fun(t;n)
Date html generated:
2018_05_21-PM-10_19_24
Last ObjectModification:
2017_07_26-PM-06_36_59
Theory : eval!all
Home
Index