Nuprl Lemma : satisfies-poly-constraints_wf
∀[f:ℤ ⟶ ℤ]. ∀[X:polynomial-constraints()]. (satisfies-poly-constraints(f;X) ∈ ℙ)
Proof
Definitions occuring in Statement :
satisfies-poly-constraints: satisfies-poly-constraints(f;X),
polynomial-constraints: polynomial-constraints(),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
satisfies-poly-constraints: satisfies-poly-constraints(f;X),
polynomial-constraints: polynomial-constraints(),
prop: ℙ,
and: P ∧ Q,
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
iPolynomial: iPolynomial(),
so_apply: x[s]
Lemmas referenced :
polynomial-constraints_wf,
le_wf,
ipolynomial-term_wf,
int_term_value_wf,
equal-wf-T-base,
l_member_wf,
iPolynomial_wf,
l_all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
productEquality,
lemma_by_obid,
isectElimination,
hypothesis,
hypothesisEquality,
lambdaEquality,
lambdaFormation,
setElimination,
rename,
intEquality,
baseClosed,
setEquality,
because_Cache,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
functionEquality
Latex:
\mforall{}[f:\mBbbZ{} {}\mrightarrow{} \mBbbZ{}]. \mforall{}[X:polynomial-constraints()]. (satisfies-poly-constraints(f;X) \mmember{} \mBbbP{})
Date html generated:
2016_05_14-AM-07_07_56
Last ObjectModification:
2016_01_14-PM-08_41_23
Theory : omega
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