Nuprl Lemma : eqff_assert_2
∀[b:Decision]. uiff(b = ff ∈ Decision;¬↑b)
Proof
Definitions occuring in Statement :
decision: Decision,
assert: ↑b,
bfalse: ff,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
not: ¬A,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
decision: Decision,
assert: ↑b,
bfalse: ff,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
isl: isl(x),
prop: ℙ,
subtype_rel: A ⊆r B,
top: Top,
true: True
Lemmas referenced :
btrue_wf,
bfalse_wf,
and_wf,
equal_wf,
top_wf,
isl_wf,
btrue_neq_bfalse,
true_wf,
it_wf,
unit_wf2,
not_wf,
false_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
unionElimination,
thin,
sqequalRule,
independent_pairFormation,
lambdaFormation,
lemma_by_obid,
hypothesis,
equalitySymmetry,
dependent_set_memberEquality,
equalityTransitivity,
isectElimination,
unionEquality,
hypothesisEquality,
applyEquality,
lambdaEquality,
setElimination,
rename,
productElimination,
setEquality,
independent_functionElimination,
voidElimination,
dependent_functionElimination,
inlEquality,
inrEquality,
isect_memberEquality,
voidEquality,
natural_numberEquality,
because_Cache,
independent_pairEquality,
axiomEquality
Latex:
\mforall{}[b:Decision]. uiff(b = ff;\mneg{}\muparrow{}b)
Date html generated:
2016_05_15-PM-01_44_24
Last ObjectModification:
2015_12_27-AM-00_10_37
Theory : basic
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