Nuprl Lemma : eq_bool_ff
∀[b:𝔹]. b =b ff = ¬bb
Proof
Definitions occuring in Statement : 
eq_bool: p =b q
, 
bnot: ¬bb
, 
bfalse: ff
, 
bool: 𝔹
, 
uall: ∀[x:A]. B[x]
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
implies: P 
⇒ Q
, 
not: ¬A
, 
false: False
, 
prop: ℙ
, 
rev_implies: P 
⇐ Q
, 
assert: ↑b
, 
ifthenelse: if b then t else f fi 
, 
bfalse: ff
, 
uiff: uiff(P;Q)
Lemmas referenced : 
iff_imp_equal_bool, 
eq_bool_wf, 
bfalse_wf, 
bnot_wf, 
assert_elim, 
btrue_neq_bfalse, 
assert_wf, 
equal_wf, 
bool_wf, 
false_wf, 
not_wf, 
assert_of_eq_bool, 
assert_of_bnot, 
iff_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
independent_isectElimination, 
independent_pairFormation, 
lambdaFormation, 
addLevel, 
levelHypothesis, 
equalityTransitivity, 
equalitySymmetry, 
independent_functionElimination, 
voidElimination, 
sqequalRule, 
productElimination, 
impliesFunctionality, 
because_Cache
Latex:
\mforall{}[b:\mBbbB{}].  b  =b  ff  =  \mneg{}\msubb{}b
Date html generated:
2016_05_15-PM-03_26_15
Last ObjectModification:
2015_12_27-PM-01_07_23
Theory : general
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