Nuprl Lemma : WCPR_wf
∀[F:ℝ ⟶ 𝔹]. ∀[x:ℝ]. ∀[G:n:ℕ+ ⟶ {y:ℝ| x = y ∈ (ℕ+n ⟶ ℤ)} ]. (WCPR(F;x;G) ∈ ℕ+)
Proof
Definitions occuring in Statement :
WCPR: WCPR(F;x;G),
real: ℝ,
int_seg: {i..j-},
nat_plus: ℕ+,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
WCPR: WCPR(F;x;G),
all: ∀x:A. B[x],
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
and: P ∧ Q,
prop: ℙ,
real: ℝ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
le: A ≤ B,
false: False,
not: ¬A,
implies: P ⇒ Q
Lemmas referenced :
WCP_wf,
real_wf,
regularize-k-regular,
less_than_wf,
regularize_wf,
nat_plus_wf,
regular-int-seq_wf,
subtype_rel_sets,
equal_wf,
int_seg_wf,
subtype_rel_dep_function,
int_seg_subtype_nat_plus,
false_wf,
subtype_rel_self,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
lambdaEquality,
applyEquality,
functionExtensionality,
hypothesisEquality,
hypothesis,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
imageMemberEquality,
baseClosed,
isectElimination,
functionEquality,
because_Cache,
intEquality,
setElimination,
rename,
independent_isectElimination,
lambdaFormation,
setEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[F:\mBbbR{} {}\mrightarrow{} \mBbbB{}]. \mforall{}[x:\mBbbR{}]. \mforall{}[G:n:\mBbbN{}\msupplus{} {}\mrightarrow{} \{y:\mBbbR{}| x = y\} ]. (WCPR(F;x;G) \mmember{} \mBbbN{}\msupplus{})
Date html generated:
2017_10_03-AM-10_06_22
Last ObjectModification:
2017_09_12-AM-09_58_33
Theory : reals
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