Nuprl Lemma : btrue_neq_bfalse
¬tt = ff
Proof
Definitions occuring in Statement :
bfalse: ff,
btrue: tt,
bool: 𝔹,
not: ¬A,
equal: s = t ∈ T
Definitions unfolded in proof :
not: ¬A,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
uimplies: b supposing a,
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T},
true: True,
false: False
Lemmas referenced :
equal_wf,
bool_wf,
btrue_wf,
bfalse_wf,
ifthenelse_wf,
subtype_base_sq,
int_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
applyEquality,
lambdaEquality,
hypothesisEquality,
intEquality,
natural_numberEquality,
equalityUniverse,
levelHypothesis,
sqequalRule,
instantiate,
cumulativity,
independent_isectElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
voidElimination,
promote_hyp
Latex:
\mneg{}tt = ff
Date html generated:
2016_05_13-PM-03_55_30
Last ObjectModification:
2015_12_26-AM-10_53_13
Theory : bool_1
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