Peter, I'm starting to think, both by your oddly worded posts and by your spelling, that you are in over your head. Let me clarify, because, while everyone here has been more or less correct with explaining this concept, you still seem to be confused.
These people are trying to explain to you the difference in sharpness between sensors, as it applies to your cloudy question. Larger sensors will have bigger, crisper pixels in the output image, due in part to lens resolution, actual pixel size and ability to collect photons, and also the fact that bigger pixels means sharper received image through the low pass (anti-alias) filter placed in front of the sensor.
A smaller 12 megapixel image from a full-frame 5D, enlarged to print at the size of an 18 megapixel printed image from a 7D will have much better resolution than a 12 megapixel APS-C image enlarged to the size of the 7D's image. This is because full-frame images are inherently sharper at a pixel level (100% zoom in photoshop). You will notice that, side-by-side, APS-C cameras, including the 7D, will be slightly softer in most cases at the pixel level, which means that a sharp 100% enlargement of a 5D image might, and in most cases will, be very sharp, whereas a 100% enlargement of a crop sensor image will be slightly less sharp.
So to answer your original question, an enlarged 12mp 5D image could and would be at least as sharp as a 7D image printed natively (at 300, 250, 200dpi, take your pick). This won't always be the case, I've made impressive 24" wide prints with the 7D, which were @ 250dpi, and I have also made very impressive 18-24" wide prints from a 5D, that were upsampled (digitally enlarged), and sharpened, post processed from there.
There is no mathmatical equation that universally describes detail comparing crop and full-frame sensors. Each camera and lens combination will give you different resolving capabilities.
But, generally, full-frame sensors, even smaller 12mp sensors, give sharper images than their current higher megapixel crop-sensor cousins. Sharp enough, that many people can argue that a 12mp 5D will give you equal or even better enlargements on print than an 18mp 7D.
Hope that clears things up.
I did not make this up, I read it years ago from a credible site.
BTW, what exactly are your qualifications? I mean what formal engineering training do you have in digital imagry? What you have written, and no matter how convinced you are, your understanding is still only your own opinion.
BTW grow up!