Nuprl Lemma : rational-form-has-value
∀[r:ℤ ⋃ (ℤ × ℤ-o)]. has-valueall(r)
Proof
Definitions occuring in Statement :
int_nzero: ℤ-o,
has-valueall: has-valueall(a),
b-union: A ⋃ B,
uall: ∀[x:A]. B[x],
product: x:A × B[x],
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
all: ∀x:A. B[x],
int_nzero: ℤ-o,
has-valueall: has-valueall(a),
has-value: (a)↓
Lemmas referenced :
valueall-type-has-valueall,
b-union_wf,
int_nzero_wf,
bunion-valueall-type,
int-valueall-type,
product-valueall-type,
set-valueall-type,
nequal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
productEquality,
hypothesis,
independent_isectElimination,
because_Cache,
sqequalRule,
lambdaEquality,
independent_functionElimination,
lambdaFormation,
hypothesisEquality,
natural_numberEquality,
axiomSqleEquality
Latex:
\mforall{}[r:\mBbbZ{} \mcup{} (\mBbbZ{} \mtimes{} \mBbbZ{}\msupminus{}\msupzero{})]. has-valueall(r)
Date html generated:
2016_05_15-PM-10_37_09
Last ObjectModification:
2015_12_27-PM-08_00_42
Theory : rationals
Home
Index