Nuprl Lemma : no_repeats-pcs-mon-vars
∀X:polynomial-constraints(). no_repeats(ℤ List;pcs-mon-vars(X))
Proof
Definitions occuring in Statement :
pcs-mon-vars: pcs-mon-vars(X),
polynomial-constraints: polynomial-constraints(),
no_repeats: no_repeats(T;l),
list: T List,
all: ∀x:A. B[x],
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
polynomial-constraints: polynomial-constraints(),
pcs-mon-vars: pcs-mon-vars(X),
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
iPolynomial: iPolynomial(),
so_lambda: λ2x.t[x],
int_seg: {i..j-},
sq_stable: SqStable(P),
implies: P ⇒ Q,
lelt: i ≤ j < k,
and: P ∧ Q,
squash: ↓T,
guard: {T},
so_apply: x[s],
iMonomial: iMonomial(),
prop: ℙ,
top: Top,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
no_repeats-polynomial-mon-vars,
list_accum_cons_lemma,
list_accum_nil_lemma,
no_repeats_wf,
list_induction,
polynomial-constraints_wf,
no_repeats_singleton,
polynomial-mon-vars_wf,
nil_wf,
cons_wf,
subtype_rel_self,
sorted_wf,
int_nzero_wf,
subtype_rel_product,
le_weakening2,
less_than_transitivity2,
sq_stable__le,
select_wf,
imonomial-less_wf,
length_wf,
int_seg_wf,
all_wf,
iMonomial_wf,
subtype_rel_set,
iPolynomial_wf,
subtype_rel_list,
top_wf,
list_wf,
list_accum_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
cut,
hypothesis,
dependent_functionElimination,
hypothesisEquality,
lemma_by_obid,
isectElimination,
productEquality,
intEquality,
because_Cache,
applyEquality,
independent_isectElimination,
lambdaEquality,
natural_numberEquality,
setElimination,
rename,
independent_functionElimination,
introduction,
imageMemberEquality,
baseClosed,
imageElimination,
setEquality,
isect_memberEquality,
voidElimination,
voidEquality,
functionEquality
Latex:
\mforall{}X:polynomial-constraints(). no\_repeats(\mBbbZ{} List;pcs-mon-vars(X))
Date html generated:
2016_05_14-AM-07_10_23
Last ObjectModification:
2016_01_14-PM-08_40_57
Theory : omega
Home
Index