Prove two adjacent numbers are equal.

Prove4Equals5.groovy

//Prove 4 == 5

def lhs = 4
def rhs = 5

assert -20 == -20
assert 16 - 36 == 25 - 45
assert lhs ** 2 - 36 == rhs ** 2 - 45
assert lhs ** 2 - 2 * lhs * ( 9 / 2 ) == rhs ** 2 - 2 * rhs *( 9 / 2 )
assert lhs ** 2 - 2 * lhs * ( 9 / 2 ) + ( 9 / 2 ) ** 2 == rhs ** 2 - 2 * rhs * ( 9 / 2 ) + ( 9 / 2 ) ** 2
assert ( lhs - ( 9 / 2 ) ) ** 2 == ( rhs - ( 9 / 2 ) ) ** 2 //[(a-b)**2 == a**2 + b**2 - 2*a*b]
assert Math.sqrt( ( lhs - ( 9 / 2 ) ) ** 2 ) == Math.sqrt( ( rhs - ( 9 / 2 ) ) ** 2 )
assert Math.abs( lhs - ( 9 / 2 ) ) == Math.abs( rhs - ( 9 / 2 ) )

//Caveat
assert lhs - 9 / 2 != rhs - 9 / 2

//Hence
assert lhs != rhs