Nuprl Lemma : int_term_to_ipoly-sub
∀[a,b:Top]. (int_term_to_ipoly(a (-) b) ~ add_ipoly(int_term_to_ipoly(a);minus-poly(int_term_to_ipoly(b))))
Proof
Definitions occuring in Statement :
int_term_to_ipoly: int_term_to_ipoly(t),
minus-poly: minus-poly(p),
add_ipoly: add_ipoly(p;q),
itermSubtract: left (-) right,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
int_term_to_ipoly: int_term_to_ipoly(t),
itermSubtract: left (-) right,
int_term_ind: int_term_ind,
uall: ∀[x:A]. B[x],
member: t ∈ T
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
sqequalAxiom,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[a,b:Top].
(int\_term\_to\_ipoly(a (-) b) \msim{} add\_ipoly(int\_term\_to\_ipoly(a);minus-poly(int\_term\_to\_ipoly(b))))
Date html generated:
2017_09_29-PM-05_55_30
Last ObjectModification:
2017_05_10-PM-04_18_28
Theory : omega
Home
Index