-
Notifications
You must be signed in to change notification settings - Fork 2
/
Copy pathdecomp_regress.txt
203 lines (162 loc) · 2.5 KB
/
decomp_regress.txt
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
Debug: apply 3.
Debug: intro x.
apply x.
Debug: intros x y.
apply x.
Debug: intros H y.
apply y.
Debug: intros x H.
apply x.
Debug: intros H H0 x.
apply x.
Debug: apply @eq_refl.
Debug: reflexivity.
Debug: reflexivity.
Debug: apply (eq_rect (A:=nat)).
Debug: rewrite eq_refl.
apply tt.
Debug: rewrite <- eq_refl.
apply I.
Debug: intros x H.
rewrite H.
rewrite <- H.
reflexivity.
Debug: intros a b H H0.
rewrite H0 in H.
apply H.
Debug:
intros a b H H0.
rewrite H0 in H.
rewrite <- H0 in H.
rewrite H0 in H.
apply H.
Debug: intros a b H H0.
reflexivity.
Debug: intros a b H H0.
reflexivity.
Debug: intros a b H.
left.
apply H.
Debug: intros a b H.
right.
apply H.
Debug: intros a b H H0.
split.
- apply H.
- apply H0.
Debug: split.
- left.
reflexivity.
- right.
reflexivity.
Debug:
intro x.
induction x as [ |x0 IHx].
- reflexivity.
- simpl.
rewrite IHx.
reflexivity.
Debug:
intros X xs.
induction xs as [ |a xs0 IHxs]; intros ys0 zs0.
- reflexivity.
- simpl.
rewrite
(IHxs ys0 zs0).
reflexivity.
Debug:
intros P Q H.
induction H as [H0|H0].
- left.
apply H0.
- right.
apply H0.
Debug:
intros A l.
induction l as [ |a l0 IHl].
- reflexivity.
- simpl.
rewrite
(rev_unit (rev l0) a).
simpl.
rewrite IHl.
reflexivity.
Debug:
intro n.
induction n as [ |n' H].
- intro H.
left.
reflexivity.
- intro H0.
right.
apply
(not_eq_sym (O_S n')).
Debug: intros P H.
induction H as [].
Debug:
intros A B H H0.
induction H as [H1|H1].
- induction H0 as [H2|H2].
+ left.
split.
* apply H1.
* apply H2.
+ right.
intro H3.
induction H3 as [H4 H5].
* apply H2 in H5.
induction H5 as [].
- induction H0 as [H2|H2]; right; intro H3.
+ induction H3 as [H4 H5].
* apply H1 in H4.
induction H4 as [].
+ induction H3 as [H4 H5].
* apply H2 in H5.
induction H5 as [].
Debug:
intro H.
induction H as [x p].
- exists x.
rewrite
(Nat.add_comm x 0) in p.
apply p.
Debug: intros x P.
split; symmetry; apply P.
Debug: exists 0.
split; intros x y H.
- apply H.
- symmetry.
apply H.
Debug:
intros X xs.
induction xs as [ |a xs0 IHxs]; intros ys0 H0; simpl.
- rewrite <-
(rev_involutive ys0).
simpl.
rewrite H0.
reflexivity.
- rewrite <-
(rev_involutive ys0).
simpl.
rewrite H0.
reflexivity.
Debug: auto.
Debug: auto.
Debug: auto.
Debug: auto.
Debug: auto.
Debug: auto.
Debug:
intros x y z.
induction x as [ |x0 IHx].
- auto.
- simpl.
rewrite IHx.
auto.
Debug: intro x.
omega.
Debug: intros x y H.
intro H0.
omega.
Debug: intros z H.
lia.