Nuprl Lemma : free-from-atom-outr2
∀[B,A:Type]. ∀[x:B + A]. ∀[a:Atom1]. (a#outr(x):A) supposing ((¬↑isl(x)) and a#x:B + 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],
not: ¬A,
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
top: Top,
prop: ℙ
Lemmas referenced :
free-from-atom-outr,
subtype_rel_union,
top_wf,
not_wf,
assert_wf,
isl_wf,
free-from-atom_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
because_Cache,
independent_isectElimination,
lambdaEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
freeFromAtomApplication,
freeFromAtomTriviality,
unionEquality,
freeFromAtomAxiom,
equalityTransitivity,
equalitySymmetry,
atomnEquality,
universeEquality
Latex:
\mforall{}[B,A:Type]. \mforall{}[x:B + A]. \mforall{}[a:Atom1]. (a\#outr(x):A) supposing ((\mneg{}\muparrow{}isl(x)) and a\#x:B + A)
Date html generated:
2016_05_13-PM-03_21_32
Last ObjectModification:
2015_12_26-AM-09_11_53
Theory : atom_1
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