Nuprl Lemma : add-ipoly_wf1
∀[p,q:iMonomial() List]. (add-ipoly(p;q) ∈ iMonomial() List)
Proof
Definitions occuring in Statement :
add-ipoly: add-ipoly(p;q),
iMonomial: iMonomial(),
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
subtype_rel: A ⊆r B,
or: P ∨ Q,
add-ipoly: add-ipoly(p;q),
has-value: (a)↓,
ifthenelse: if b then t else f fi ,
btrue: tt,
cons: [a / b],
colength: colength(L),
so_lambda: λ2x y.t[x; y],
top: Top,
so_apply: x[s1;s2],
squash: ↓T,
sq_stable: SqStable(P),
uiff: uiff(P;Q),
and: P ∧ Q,
le: A ≤ B,
not: ¬A,
less_than': less_than'(a;b),
true: True,
nil: [],
it: ⋅,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
less_than: a < b,
subtract: n - m,
bfalse: ff,
bool: 𝔹,
unit: Unit,
exists: ∃x:A. B[x],
bnot: ¬bb,
assert: ↑b,
has-valueall: has-valueall(a),
callbyvalueall: callbyvalueall,
int_nzero: ℤ-o,
iMonomial: iMonomial(),
nequal: a ≠ b ∈ T ,
pi1: fst(t),
pi2: snd(t),
imonomial-le: imonomial-le(m1;m2),
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
decidable: Dec(P),
istype: istype(T)
Lemmas referenced :
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
nat_wf,
colength_wf_list,
iMonomial_wf,
list_wf,
list-cases,
value-type-has-value,
list-value-type,
nil_wf,
null_nil_lemma,
product_subtype_list,
spread_cons_lemma,
istype-void,
sq_stable__le,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-associates,
istype-int,
add-zero,
zero-add,
le-add-cancel,
int_subtype_base,
subtract-1-ge-0,
subtype_base_sq,
set_subtype_base,
le_wf,
add-commutes,
add-swap,
cons_wf,
null_cons_lemma,
imonomial-le_wf,
eqtt_to_assert,
eqff_to_assert,
bool_cases_sqequal,
bool_wf,
bool_subtype_base,
assert-bnot,
evalall-reduce,
int-valueall-type,
nequal_wf,
set-valueall-type,
subtype_rel_self,
sorted_wf,
int_nzero_wf,
product-valueall-type,
list-valueall-type,
valueall-type-has-valueall,
equal_wf,
int-value-type,
minus-minus,
less-iff-le,
not-ge-2,
subtract_wf,
minus-one-mul-top,
minus-one-mul,
minus-add,
condition-implies-le,
not-le-2,
false_wf,
decidable__le,
equal-wf-T-base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
thin,
Error :lambdaFormation_alt,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
sqequalRule,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
independent_functionElimination,
voidElimination,
Error :universeIsType,
Error :lambdaEquality_alt,
dependent_functionElimination,
Error :isect_memberEquality_alt,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
Error :equalityIsType3,
applyEquality,
unionElimination,
callbyvalueReduce,
voidEquality,
because_Cache,
promote_hyp,
hypothesis_subsumption,
productElimination,
applyLambdaEquality,
imageMemberEquality,
baseClosed,
imageElimination,
addEquality,
Error :equalityIsType4,
Error :equalityIsType1,
instantiate,
cumulativity,
intEquality,
Error :dependent_set_memberEquality_alt,
minusEquality,
equalityElimination,
Error :dependent_pairFormation_alt,
lambdaFormation,
setEquality,
lambdaEquality,
dependent_pairFormation,
dependent_set_memberEquality,
independent_pairEquality,
int_eqEquality,
independent_pairFormation,
isect_memberEquality
Latex:
\mforall{}[p,q:iMonomial() List]. (add-ipoly(p;q) \mmember{} iMonomial() List)
Date html generated:
2019_06_20-PM-00_45_10
Last ObjectModification:
2018_10_02-PM-11_35_52
Theory : omega
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