import proveit %begin demonstrations
from proveit import ExprRange, ExprTuple, IndexedVar from proveit import a, b, c, i, j, k, l, x, y, z
from proveit import defaults defaults.automation = False
ExprRange(k, IndexedVar(x, k), i, j)._free_var_ranges()
ExprRange(l, ExprRange(k, IndexedVar(x, (k, l)), i, j), a, b)
ExprRange(l, ExprRange(k, IndexedVar(x, (k, l)), i, j), a, b)._free_var_ranges()
ExprRange(l, ExprRange(k, IndexedVar(x, (l, k)), i, j), a, b)._free_var_ranges()
%end demonstrations