Nuprl Lemma : free-from-atom-outr
∀[A:Type]. ∀[x:Top + A]. ∀[a:Atom1]. (a#outr(x):A) supposing ((¬↑isl(x)) and a#x:Top + A)
Proof
Definitions occuring in Statement :
free-from-atom: a#x:T,
atom: Atom$n,
outr: outr(x),
assert: ↑b,
isl: isl(x),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
not: ¬A,
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
isl: isl(x),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
outr: outr(x),
not: ¬A,
implies: P ⇒ Q,
true: True,
false: False,
bfalse: ff,
prop: ℙ,
all: ∀x:A. B[x]
Lemmas referenced :
not_wf,
assert_wf,
isl_wf,
top_wf,
free-from-atom_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
unionElimination,
thin,
sqequalHypSubstitution,
sqequalRule,
independent_functionElimination,
natural_numberEquality,
voidElimination,
rename,
freeFromAtomAxiom,
hypothesis,
extract_by_obid,
isectElimination,
hypothesisEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
unionEquality,
atomnEquality,
universeEquality,
inrEquality,
freeFromAtomApplication,
freeFromAtomTriviality,
lambdaEquality,
lambdaFormation,
dependent_functionElimination,
cumulativity
Latex:
\mforall{}[A:Type]. \mforall{}[x:Top + A]. \mforall{}[a:Atom1]. (a\#outr(x):A) supposing ((\mneg{}\muparrow{}isl(x)) and a\#x:Top + A)
Date html generated:
2019_06_20-AM-11_20_25
Last ObjectModification:
2018_08_21-PM-01_52_37
Theory : atom_1
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