Nuprl Lemma : minus-monomial_wf
∀[m:iMonomial()]. (minus-monomial(m) ∈ iMonomial())
Proof
Definitions occuring in Statement :
minus-monomial: minus-monomial(m),
iMonomial: iMonomial(),
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
iMonomial: iMonomial(),
uall: ∀[x:A]. B[x],
member: t ∈ T,
minus-monomial: minus-monomial(m),
int_nzero: ℤ-o,
nequal: a ≠ b ∈ T ,
prop: ℙ,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
not: ¬A,
implies: P ⇒ Q,
subtract: n - m,
true: True,
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T},
false: False,
uiff: uiff(P;Q),
and: P ∧ Q
Lemmas referenced :
nequal_wf,
int_nzero_wf,
list_wf,
sorted_wf,
istype-int,
subtract_wf,
minus-zero,
minus-one-mul,
zero-add,
add-zero,
trivial-cancel,
subtype_base_sq,
int_subtype_base,
int_nzero_properties
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
productElimination,
thin,
independent_pairEquality,
Error :dependent_set_memberEquality_alt,
minusEquality,
sqequalHypSubstitution,
setElimination,
rename,
hypothesisEquality,
hypothesis,
Error :universeIsType,
extract_by_obid,
isectElimination,
intEquality,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :productIsType,
Error :setIsType,
independent_isectElimination,
Error :lambdaEquality_alt,
Error :lambdaFormation_alt,
addEquality,
multiplyEquality,
because_Cache,
instantiate,
cumulativity,
dependent_functionElimination,
independent_functionElimination,
voidElimination,
Error :equalityIstype,
Error :inhabitedIsType
Latex:
\mforall{}[m:iMonomial()]. (minus-monomial(m) \mmember{} iMonomial())
Date html generated:
2019_06_20-PM-00_45_38
Last ObjectModification:
2018_12_07-AM-10_21_14
Theory : omega
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