Nuprl Lemma : band_bor_absorption
∀[a,b:Top]. (a ∨b(a ∧b b) ~ a ∧b tt)
Proof
Definitions occuring in Statement :
bor: p ∨bq,
band: p ∧b q,
btrue: tt,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bor: p ∨bq,
ifthenelse: if b then t else f fi ,
btrue: tt,
it: ⋅,
band: p ∧b q,
bfalse: ff,
all: ∀x:A. B[x],
implies: P ⇒ Q,
top: Top,
has-value: (a)↓,
prop: ℙ
Lemmas referenced :
top_wf,
equal_wf,
has-value_wf_base,
is-exception_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
hypothesisEquality,
thin,
because_Cache,
lambdaFormation,
isect_memberEquality,
voidElimination,
voidEquality,
extract_by_obid,
hypothesis,
sqequalSqle,
divergentSqle,
callbyvalueDecide,
sqequalHypSubstitution,
unionEquality,
unionElimination,
sqleReflexivity,
isectElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
decideExceptionCases,
axiomSqleEquality,
exceptionSqequal,
baseApply,
closedConclusion,
baseClosed,
sqequalAxiom
Latex:
\mforall{}[a,b:Top]. (a \mvee{}\msubb{}(a \mwedge{}\msubb{} b) \msim{} a \mwedge{}\msubb{} tt)
Date html generated:
2017_04_14-AM-07_29_49
Last ObjectModification:
2017_02_27-PM-02_58_28
Theory : bool_1
Home
Index