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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