Nuprl Lemma : real_term_polynomial
∀t:int_term(). ipolynomial-term(int_term_to_ipoly(t)) ≡ t
Proof
Definitions occuring in Statement :
req_int_terms: t1 ≡ t2,
int_term_to_ipoly: int_term_to_ipoly(t),
ipolynomial-term: ipolynomial-term(p),
int_term: int_term(),
all: ∀x:A. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
iPolynomial: iPolynomial(),
so_apply: x[s],
implies: P ⇒ Q,
all: ∀x:A. B[x],
int_term_to_ipoly: int_term_to_ipoly(t),
itermConstant: "const",
int_term_ind: int_term_ind,
itermVar: vvar,
itermAdd: left (+) right,
prop: ℙ,
itermSubtract: left (-) right,
itermMultiply: left (*) right,
itermMinus: "-"num,
guard: {T},
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
sq_type: SQType(T),
false: False,
not: ¬A,
req_int_terms: t1 ≡ t2,
ipolynomial-term: ipolynomial-term(p),
top: Top,
ifthenelse: if b then t else f fi ,
btrue: tt,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
bfalse: ff,
imonomial-term: imonomial-term(m),
real_term_value: real_term_value(f;t),
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
rsub: x - y
Lemmas referenced :
int_term-induction,
req_int_terms_wf,
ipolynomial-term_wf,
int_term_to_ipoly_wf,
iPolynomial_wf,
int_term_wf,
decidable__equal_int,
subtype_base_sq,
int_subtype_base,
real_wf,
null_nil_lemma,
real_term_value_const_lemma,
req_weakening,
int-to-real_wf,
null_cons_lemma,
spread_cons_lemma,
list_accum_nil_lemma,
real_term_value_wf,
itermConstant_wf,
list_accum_cons_lemma,
rmul-identity1,
add-ipoly_wf1,
itermAdd_wf,
itermAdd_functionality_wrt_req,
add_ipoly-sq,
req_int_terms_functionality,
add-ipoly-req,
req_int_terms_weakening,
add_ipoly_wf,
minus-poly_wf,
itermSubtract_wf,
itermMinus_wf,
uiff_transitivity,
req_int_terms_transitivity,
minus-poly-req,
itermMinus_functionality_wrt_req,
radd_wf,
rminus_wf,
mul_ipoly_wf,
itermMultiply_wf,
mul-ipoly_wf,
mul_poly-sq,
mul-ipoly-req,
itermMultiply_functionality_wrt_req
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
sqequalRule,
lambdaEquality,
hypothesisEquality,
hypothesis,
applyEquality,
setElimination,
rename,
independent_functionElimination,
lambdaFormation,
intEquality,
because_Cache,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
instantiate,
cumulativity,
independent_isectElimination,
int_eqReduceFalseSq,
functionEquality,
isect_memberEquality,
voidElimination,
voidEquality,
functionExtensionality,
productElimination
Latex:
\mforall{}t:int\_term(). ipolynomial-term(int\_term\_to\_ipoly(t)) \mequiv{} t
Date html generated:
2017_10_02-PM-07_20_30
Last ObjectModification:
2017_07_28-AM-07_21_36
Theory : reals
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