### 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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