continuous_lambda [ T : TYPE FROM real ] : THEORY BEGIN IMPORTING continuous_functions[T],VAR continuous_funFORALL (x:T) : f(x) > 0TYPE = (pos_continuous?)VAR nz_continuous_funVAR pos_continuous_funVAR TVAR realVAR nzrealVAR natLEMMA LAMBDA (x):x)LEMMA LAMBDA (x):k)LEMMA LAMBDA (x):f(x)+g(x))LEMMA LAMBDA (x):f(x)-g(x))LEMMA LAMBDA (x):-f(x))LEMMA LAMBDA (x):f(x)*g(x))LEMMA LAMBDA (x):f(x)/nzf(x))LEMMA LAMBDA (x):k*f(x))LEMMA LAMBDA (x):f(x)/nzk)LEMMA LAMBDA (x):k/nzf(x))LEMMA LAMBDA (x):f(x)^n) LEMMA LAMBDA (x):sq(f(x)))IMPORTING sqrt_derivative,LEMMA LAMBDA (x):sqrt(pf(x)))LEMMA LAMBDA (x):abs(f(x)))LEMMA LAMBDA (x):max(f(x),g(x)))LEMMA LAMBDA (x):min(f(x),g(x)))END continuous_lambdaquality 86%
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