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X-ray pulses can be generated using a probe laser pulse reflection off a relativistic electron mirror (REM). The main problem preventing experimental realization of this scheme is an absence of accelerating laser pulses with sharp enough fronts. We consider laser pulse shaping using plasma layers with thickness of about laser wavelength and density of about 2-10 times larger than the critical density. Here, petawatt class electromagnetic pulses with sharp fronts can be produced. Generation of REM with such pulses was simulated and reflection of counter-propagating probe pulse was studied giving x-ray coherent pulse (wavelength about 10 nm) with attosecond length and power of about 100 GW.