Nuprl Lemma : nonneg-monomial_wf
∀[m:iMonomial()]. (nonneg-monomial(m) ∈ 𝔹)
Proof
Definitions occuring in Statement :
nonneg-monomial: nonneg-monomial(m),
iMonomial: iMonomial(),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nonneg-monomial: nonneg-monomial(m),
iMonomial: iMonomial(),
int_nzero: ℤ-o,
all: ∀x:A. B[x],
or: P ∨ Q,
uimplies: b supposing a,
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T},
uiff: uiff(P;Q),
and: P ∧ Q,
bfalse: ff,
band: p ∧b q,
ifthenelse: if b then t else f fi
Lemmas referenced :
le_int_wf,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
band_wf,
btrue_wf,
assert_of_le_int,
even-int-list_wf,
bfalse_wf,
iMonomial_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
spreadEquality,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
hypothesisEquality,
extract_by_obid,
isectElimination,
natural_numberEquality,
setElimination,
rename,
hypothesis,
dependent_functionElimination,
unionElimination,
instantiate,
cumulativity,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
axiomEquality,
Error :universeIsType
Latex:
\mforall{}[m:iMonomial()]. (nonneg-monomial(m) \mmember{} \mBbbB{})
Date html generated:
2019_06_20-PM-00_45_51
Last ObjectModification:
2019_04_08-PM-01_59_11
Theory : omega
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