Nuprl Lemma : free-from-atom-Id-rw
∀[i:Id]. ∀[a:Atom1]. uiff(a#i:Id;True)
Proof
Definitions occuring in Statement :
Id: Id,
free-from-atom: a#x:T,
atom: Atom$n,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
true: True
Definitions unfolded in proof :
Id: Id,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
true: True,
prop: ℙ
Lemmas referenced :
free-from-atom_wf,
istype-true
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
independent_pairFormation,
natural_numberEquality,
sqequalRule,
sqequalHypSubstitution,
axiomEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
Error :universeIsType,
extract_by_obid,
isectElimination,
thin,
atomnEquality,
hypothesisEquality,
freeFromAtom1Atom2,
freeFromAtomAxiom,
productElimination,
independent_pairEquality,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies,
Error :inhabitedIsType
Latex:
\mforall{}[i:Id]. \mforall{}[a:Atom1]. uiff(a\#i:Id;True)
Date html generated:
2019_06_20-PM-01_58_27
Last ObjectModification:
2019_03_27-PM-03_13_18
Theory : decidable!equality
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