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answered 2024-06-28 10:10:15 +0100
Alternative : Sympy's subsis recursive :
subs
sage: Dt_E._sympy_().subs({u.lhs()._sympy_():u.rhs()._sympy_() for u in (E*L==1/2, E*E==-1/6, L*L==-1/2, E*L*c==c*1/2)})._sage_() 1/6*t
HTH,