Nuprl Lemma : real-has-valueall
∀[x:ℝ]. has-valueall(x)
Proof
Definitions occuring in Statement :
real: ℝ,
has-valueall: has-valueall(a),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
real: ℝ,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
has-valueall: has-valueall(a),
has-value: (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 :
function-valueall-type,
nat_plus_wf,
valueall-type-has-valueall,
real_wf,
less_than_wf,
int-value-type,
value-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
extract_by_obid,
isectElimination,
hypothesis,
sqequalRule,
lambdaEquality,
intEquality,
independent_isectElimination,
functionEquality,
hypothesisEquality,
axiomSqleEquality,
dependent_pairFormation,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
imageMemberEquality,
baseClosed
Latex:
\mforall{}[x:\mBbbR{}]. has-valueall(x)
Date html generated:
2017_10_02-PM-07_13_17
Last ObjectModification:
2017_06_01-PM-05_52_33
Theory : reals
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