Nuprl Lemma : imonomial-cons
∀v:ℤ List. ∀u,a:ℤ. ∀f:ℤ ⟶ ℤ. (int_term_value(f;imonomial-term(<a, [u / v]>)) = int_term_value(f;imonomial-term(<a * (f\000C u), v>)) ∈ ℤ)
Proof
Definitions occuring in Statement :
imonomial-term: imonomial-term(m),
int_term_value: int_term_value(f;t),
cons: [a / b],
list: T List,
all: ∀x:A. B[x],
apply: f a,
function: x:A ⟶ B[x],
pair: <a, b>,
multiply: n * m,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
prop: ℙ,
imonomial-term: imonomial-term(m),
int_term_value: int_term_value(f;t),
top: Top,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
itermConstant: "const",
int_term_ind: int_term_ind,
itermMultiply: left (*) right,
itermVar: vvar,
squash: ↓T,
true: True
Lemmas referenced :
list_induction,
all_wf,
equal_wf,
int_term_value_wf,
imonomial-term_wf,
cons_wf,
list_wf,
list_accum_cons_lemma,
list_accum_nil_lemma,
squash_wf,
true_wf,
int_term_wf,
list_accum_wf,
itermMultiply_wf,
itermVar_wf,
itermConstant_wf,
int_term_value_mul_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
intEquality,
sqequalRule,
lambdaEquality,
functionEquality,
functionExtensionality,
applyEquality,
hypothesisEquality,
independent_pairEquality,
hypothesis,
multiplyEquality,
independent_functionElimination,
rename,
because_Cache,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
hyp_replacement,
equalitySymmetry,
imageElimination,
equalityTransitivity,
universeEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed
Latex:
\mforall{}v:\mBbbZ{} List. \mforall{}u,a:\mBbbZ{}. \mforall{}f:\mBbbZ{} {}\mrightarrow{} \mBbbZ{}. (int\_term\_value(f;imonomial-term(<a, [u / v]>)) = int\_term\_value(f;im\000Conomial-term(<a * (f u), v>)))
Date html generated:
2017_04_14-AM-08_57_49
Last ObjectModification:
2017_02_27-PM-03_41_16
Theory : omega
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