Nuprl Lemma : bor_bnot
∀[a:Top]. (a ∨b(¬ba) ~ a ∨btt)
Proof
Definitions occuring in Statement :
bor: p ∨bq
,
bnot: ¬bb
,
btrue: tt
,
uall: ∀[x:A]. B[x]
,
top: Top
,
sqequal: s ~ t
Definitions unfolded in proof :
bor: p ∨bq
,
bnot: ¬bb
,
ifthenelse: if b then t else f fi
,
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
has-value: (a)↓
,
all: ∀x:A. B[x]
,
or: P ∨ Q
,
uimplies: b supposing a
,
sq_type: SQType(T)
,
implies: P
⇒ Q
,
guard: {T}
,
uiff: uiff(P;Q)
,
and: P ∧ Q
,
btrue: tt
,
bfalse: ff
Lemmas referenced :
assert_of_bnot,
eqff_to_assert,
is-exception_wf,
has-value_wf_base,
eqtt_to_assert,
bool_subtype_base,
bool_wf,
subtype_base_sq,
bool_cases,
top_wf,
isl_wf,
injection-eta
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
sqequalSqle,
sqleRule,
thin,
divergentSqle,
callbyvalueDecide,
sqequalHypSubstitution,
hypothesis,
lemma_by_obid,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
isectElimination,
because_Cache,
unionElimination,
instantiate,
cumulativity,
independent_isectElimination,
independent_functionElimination,
productElimination,
sqleReflexivity,
baseClosed,
decideExceptionCases,
axiomSqleEquality,
exceptionSqequal,
baseApply,
closedConclusion,
hypothesisEquality,
sqequalAxiom
Latex:
\mforall{}[a:Top]. (a \mvee{}\msubb{}(\mneg{}\msubb{}a) \msim{} a \mvee{}\msubb{}tt)
Date html generated:
2016_05_13-PM-03_55_48
Last ObjectModification:
2016_01_14-PM-07_20_49
Theory : bool_1
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