我想使用QArith的交换性适当性来替换另一个表达式：
Require Import QArith.
Variable q1 q2 : Q.
Lemma l1 : q1 + q2 = q2 + q1.
Proof.
rewrite Qplus_comm. (* Fail *)
有没有办法将“Qeq”等式用作“=”？
答案 0 :(得分：0)
from collections import OrderedDict
import numpy as np
import bokeh.plotting as bk
from bokeh.plotting import figure, show, output_file
from bokeh.models import HoverTool, ColumnDataSource
bk.output_notebook() #for viz within ipython notebook
N = 20
arr2d = np.random.randint(0,10,size=(N,N))
predicted = []
actual = []
count = []
color = []
alpha = []
the_color = '#cc0000'
for col in range(N):
for rowi in range(N):
predicted.append(str(rowi))
actual.append(str(col))
count.append(arr2d[rowi,col])
a = arr2d[rowi,col]/10.0
alpha.append(a)
color.append(the_color)
source = ColumnDataSource(
data=dict(predicted=predicted, actual=actual, count=count, alphas=alpha, colors=color)
)
#THE FIX IS HERE! use `set` to dedup
correct_y_range = sorted(list(set(actual)), reverse=True)
correct_x_range = sorted(list(set(predicted)))
p = figure(title='Confusion Matrix',
x_axis_location="above", tools="resize,hover,save",
y_range=correct_y_range, x_range=correct_x_range)
p.plot_width = 600
p.plot_height = p.plot_width
rectwidth = 0.9
p.rect('predicted', 'actual', rectwidth, rectwidth, source=source,
color='colors', alpha='alphas',line_width=1, line_color='k')
p.axis.major_label_text_font_size = "12pt"
p.axis.major_label_standoff = 1
p.xaxis.major_label_orientation = np.pi/3
hover = p.select(dict(type=HoverTool))
hover.tooltips = OrderedDict([
('predicted', '@predicted'),
('actual', '@actual'),
('count', '@count'),
])
show(p)
与import matplotlib.pyplot as plt
import numpy as np
# define four sets of data here: x1, y1, yerr1, x2, y2, yerr2, etc...
fit1 = np.poly1d(np.polyfit(x1,y1,1))
xrange = np.linspace(min(x1), max(x1), num = 1000)
f, axarr = plt.subplots(2,2)
axarr[0,0].plot(xrange, fit1(xrange))
axarr[0,0].errorbar(x1, y1, yerr = yerr1, fmt = 'r.')
# and for the rest just the errorbar portion
plt.show()
不同。这是一个证明，假设它们相等导致q1 == q2，这是一个矛盾。
q1 = q2请参阅Conversion of nat to Q in Coq，其中Arthur A A显示False，并解释原因。