Nuprl Lemma : free-from-atom-atom
∀[a,b:Atom1]. uiff(b#a:Atom1;¬(a = b ∈ Atom1))
Proof
Definitions occuring in Statement :
free-from-atom: a#x:T,
atom: Atom$n,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
not: ¬A,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
equal-wf-base,
atom1_subtype_base,
free-from-atom_wf,
not_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lambdaFormation,
thin,
hypothesis,
sqequalHypSubstitution,
independent_functionElimination,
voidElimination,
extract_by_obid,
isectElimination,
atomnEquality,
hypothesisEquality,
applyEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
because_Cache,
freeFromAtomBase,
freeFromAtomAxiom,
productElimination,
independent_pairEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
hyp_replacement,
Error :applyLambdaEquality,
freeFromAtomAbsurdity
Latex:
\mforall{}[a,b:Atom1]. uiff(b\#a:Atom1;\mneg{}(a = b))
Date html generated:
2016_10_21-AM-09_36_08
Last ObjectModification:
2016_07_12-AM-05_00_09
Theory : atom_1
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