Structural Induction Proof: Basis
lTo
show P([]):
("M) length(append([], M)) = length([]) + length(M)
("M) length(append([], M)) = length([]) + length(M)
lWe
know from the definition of append that
append([], M) == M.
append([], M) == M.
lWe
also know that
length([]) == 0.
length([]) == 0.
lSo
the thing to be shown reduces to:
("M) length(M) == 0 + length(M)
which is true since the equation reduces to an identity.
("M) length(M) == 0 + length(M)
which is true since the equation reduces to an identity.