re: Is there proof that CO2 causes warming?

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isnt this why you introduce z (compressibility factor) into the equation, which becomes the real gas law rather than ideal to account for the changing density at different P&Ts?

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Yeah, the comprehensibility factor accounts for deviations from ideal behavior. Like when a gas is close to a phase change or it's critical point, low T or high P conditions. There's still a relationship between density (well volume since we're not altering the mass) and a given T and P. Just a different response than if it was high T, low P settings like the IGL is good for.