Operators are not immutable. Operator properties are dynamic and among other things affect equality!
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(1) -> f:=operator 'f
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g:=operator 'f
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test(f=g)
Type: Boolean
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test(kernels f(x) = kernels g(x))
Type: Boolean
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test(f(x)=g(x))
Type: Boolean
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name f
Type: Symbol
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name g
Type: Symbol
Change or add a property.
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display(g,(x:List OutputForm):OutputForm+->prefix('G,x)$OutputForm)
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g(x)
Type: Expression(Integer)
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test(f=g)
Type: Boolean
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test(kernels f(x) = kernels g(x))
Type: Boolean
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test(f(x)=g(x))
Type: Boolean
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name f
Type: Symbol
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name g
Type: Symbol