Nuprl Lemma : not-assert
∀[b:𝔹]. uiff(¬↑b;b = ff)
Proof
Definitions occuring in Statement :
assert: ↑b,
bfalse: ff,
bool: 𝔹,
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,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
not: ¬A,
false: False,
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
iff_imp_equal_bool,
bfalse_wf,
assert_wf,
false_wf,
not_wf,
assert_elim,
btrue_neq_bfalse,
equal_wf,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_isectElimination,
sqequalRule,
lambdaFormation,
independent_functionElimination,
voidElimination,
addLevel,
levelHypothesis,
equalityTransitivity,
equalitySymmetry,
lambdaEquality,
dependent_functionElimination,
productElimination,
independent_pairEquality,
isect_memberEquality,
axiomEquality,
because_Cache
Latex:
\mforall{}[b:\mBbbB{}]. uiff(\mneg{}\muparrow{}b;b = ff)
Date html generated:
2016_05_15-PM-03_27_11
Last ObjectModification:
2015_12_27-PM-01_08_13
Theory : general
Home
Index