Nuprl Lemma : rnonneg2_wf
∀[x:ℕ+ ⟶ ℤ]. (rnonneg2(x) ∈ ℙ)
Proof
Definitions occuring in Statement :
rnonneg2: rnonneg2(x),
nat_plus: ℕ+,
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,
rnonneg2: rnonneg2(x),
so_lambda: λ2x.t[x],
nat_plus: ℕ+,
int_upper: {i...},
le: A ≤ B,
and: P ∧ Q,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
all_wf,
nat_plus_wf,
exists_wf,
int_upper_wf,
le_wf,
less_than_transitivity1,
less_than_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
because_Cache,
setElimination,
rename,
hypothesisEquality,
multiplyEquality,
minusEquality,
natural_numberEquality,
applyEquality,
dependent_set_memberEquality,
productElimination,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
intEquality
Latex:
\mforall{}[x:\mBbbN{}\msupplus{} {}\mrightarrow{} \mBbbZ{}]. (rnonneg2(x) \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-07_01_26
Last ObjectModification:
2015_12_28-AM-00_33_57
Theory : reals
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