Nuprl Lemma : p-mu_wf
∀[P:ℕ ⟶ 𝔹]. ∀[x:ℕ + Top]. (p-mu(P;x) ∈ ℙ)
Proof
Definitions occuring in Statement :
p-mu: p-mu(P;x),
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
top: Top,
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
union: left + right
Definitions unfolded in proof :
p-mu: p-mu(P;x),
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
and: P ∧ Q,
nat: ℕ,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
so_apply: x[s],
all: ∀x:A. B[x]
Lemmas referenced :
assert_wf,
all_wf,
int_seg_wf,
not_wf,
int_seg_subtype_nat,
false_wf,
nat_wf,
top_wf,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
unionElimination,
thin,
productEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
applyEquality,
hypothesisEquality,
hypothesis,
natural_numberEquality,
setElimination,
rename,
lambdaEquality,
because_Cache,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
unionEquality,
isect_memberEquality,
functionEquality
Latex:
\mforall{}[P:\mBbbN{} {}\mrightarrow{} \mBbbB{}]. \mforall{}[x:\mBbbN{} + Top]. (p-mu(P;x) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-03_32_43
Last ObjectModification:
2015_12_27-PM-01_11_44
Theory : general
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