  It was argued by Schramm and Smirnov that the critical site percolation
exploration path on the triangular lattice converges in distribution to the
trace of chordal SLE(6). We provide here a detailed proof, which relies on
Smirnov's theorem that crossing probabilities have a conformally invariant
scaling limit (given by Cardy's formula). The version of convergence to SLE(6)
that we prove suffices for the Smirnov-Werner derivation of certain critical
percolation crossing exponents and for our analysis of the critical percolation
full scaling limit as a process of continuum nonsimple loops.
