Nuprl Lemma : d-conv_wf
∀[r:CRng]. ∀[f,g:ℕ ⟶ |r|]. (d-conv(r;f;g) ∈ ℕ ⟶ |r|)
Proof
Definitions occuring in Statement :
d-conv: d-conv(r;f;g),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
crng: CRng,
rng_car: |r|
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
nat: ℕ,
prop: ℙ,
uimplies: b supposing a,
pi1: fst(t),
pi2: snd(t),
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
nat_plus: ℕ+,
le: A ≤ B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
less_than': less_than'(a;b),
true: True,
d-conv: d-conv(r;f;g),
crng: CRng,
rng: Rng,
so_lambda: λ2x.t[x],
so_apply: x[s],
cand: A c∧ B
Lemmas referenced :
nat_wf,
two-factorizations_wf,
list-subtype-bag,
equal_wf,
subtype_rel_self,
subtype_rel_bag,
le_wf,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
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,
mul_cancel_in_le,
decidable__lt,
false_wf,
not-lt-2,
add_functionality_wrt_le,
add-commutes,
zero-add,
le-add-cancel,
less_than_wf,
itermMultiply_wf,
intformeq_wf,
int_term_value_mul_lemma,
int_formula_prop_eq_lemma,
bag-summation_wf,
rng_car_wf,
rng_plus_wf,
rng_zero_wf,
rng_times_wf,
rng_all_properties,
rng_plus_comm2,
crng_wf
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
introduction,
extract_by_obid,
hypothesis,
applyEquality,
sqequalHypSubstitution,
sqequalRule,
isectElimination,
thin,
hypothesisEquality,
setEquality,
because_Cache,
productEquality,
setElimination,
rename,
independent_isectElimination,
intEquality,
natural_numberEquality,
productElimination,
multiplyEquality,
lambdaEquality,
independent_pairEquality,
dependent_set_memberEquality,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
isect_memberFormation,
functionExtensionality,
axiomEquality,
functionEquality
Latex:
\mforall{}[r:CRng]. \mforall{}[f,g:\mBbbN{} {}\mrightarrow{} |r|]. (d-conv(r;f;g) \mmember{} \mBbbN{} {}\mrightarrow{} |r|)
Date html generated:
2018_05_21-PM-09_06_33
Last ObjectModification:
2017_07_26-PM-06_29_15
Theory : general
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