Nuprl Lemma : isaxiom-implies-not-isint
∀[t:Base]. (¬↑isint(t)) supposing ((↑isaxiom(t)) and (t)↓)
Proof
Definitions occuring in Statement :
has-value: (a)↓,
assert: ↑b,
bfalse: ff,
btrue: tt,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
isaxiom: if z = Ax then a otherwise b,
isint: isint def,
not: ¬A,
base: Base
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
has-value: (a)↓,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
bfalse: ff,
prop: ℙ,
top: Top
Lemmas referenced :
base_wf,
is-exception_wf,
has-value_wf_base,
bfalse_wf,
top_wf,
btrue_wf,
assert_wf,
true_wf,
false_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
isintCases,
divergentSqle,
hypothesis,
because_Cache,
sqequalRule,
isintReduceTrue,
natural_numberEquality,
isaxiomCases,
sqequalHypSubstitution,
voidElimination,
isectElimination,
sqequalAxiom,
isect_memberEquality,
hypothesisEquality,
lemma_by_obid,
independent_functionElimination,
voidEquality,
baseClosed,
equalityTransitivity,
equalitySymmetry,
lambdaEquality,
dependent_functionElimination
Latex:
\mforall{}[t:Base]. (\mneg{}\muparrow{}isint(t)) supposing ((\muparrow{}isaxiom(t)) and (t)\mdownarrow{})
Date html generated:
2016_05_13-PM-03_27_17
Last ObjectModification:
2016_01_14-PM-06_43_44
Theory : call!by!value_1
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