Nuprl Lemma : not_assert_elim
∀[b:𝔹]. b = ff supposing ¬↑b
Proof
Definitions occuring in Statement :
assert: ↑b,
bfalse: ff,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
assert: ↑b,
ifthenelse: if b then t else f fi ,
implies: P ⇒ Q,
not: ¬A,
true: True,
false: False,
prop: ℙ,
bfalse: ff
Lemmas referenced :
not_wf,
true_wf,
bfalse_wf,
false_wf,
assert_wf,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
thin,
sqequalHypSubstitution,
unionElimination,
equalityElimination,
sqequalRule,
lambdaFormation,
independent_functionElimination,
natural_numberEquality,
voidElimination,
extract_by_obid,
isectElimination,
hypothesis,
Error :universeIsType,
hypothesisEquality,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[b:\mBbbB{}]. b = ff supposing \mneg{}\muparrow{}b
Date html generated:
2019_06_20-AM-11_20_06
Last ObjectModification:
2018_09_26-AM-10_50_29
Theory : union
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