Nuprl Lemma : real-has-value
∀[x:ℝ]. (x)↓
Proof
Definitions occuring in Statement :
real: ℝ,
has-value: (a)↓,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
real: ℝ,
has-value: (a)↓,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
exists: ∃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
Lemmas referenced :
value-type-has-value,
value-type_wf,
int-value-type,
less_than_wf,
nat_plus_wf,
function-value-type,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
sqequalRule,
axiomSqleEquality,
hypothesis,
lemma_by_obid,
isectElimination,
lambdaEquality,
intEquality,
independent_isectElimination,
dependent_pairFormation,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
imageMemberEquality,
hypothesisEquality,
baseClosed,
functionEquality
Latex:
\mforall{}[x:\mBbbR{}]. (x)\mdownarrow{}
Date html generated:
2016_05_18-AM-06_46_57
Last ObjectModification:
2016_01_17-AM-01_45_20
Theory : reals
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