Nuprl Lemma : equal_symmetry
∀[T:Type]. ∀[x,y:T]. uiff(x = y ∈ T;y = x ∈ T)
Proof
Definitions occuring in Statement :
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
universe: Type,
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,
prop: ℙ
Lemmas referenced :
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
independent_pairFormation,
equalitySymmetry,
hypothesis,
Error :universeIsType,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
productElimination,
independent_pairEquality,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
Error :inhabitedIsType,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x,y:T]. uiff(x = y;y = x)
Date html generated:
2019_06_20-AM-11_16_38
Last ObjectModification:
2018_09_26-AM-10_24_16
Theory : core_2
Home
Index