Expression of type Conditional ¶

from the theory of proveit.numbers.modular ¶

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, L, S, c, x
from proveit.logic import Card, Equals, Forall, InSet, SetOfAll, SubsetEq
from proveit.numbers import Add, Mod, Real

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Conditional(Forall(instance_param_or_params = [S], instance_expr = Forall(instance_param_or_params = [c], instance_expr = Equals(Card(SetOfAll(instance_param_or_params = sub_expr1, instance_element = Mod(Add(x, c), L), domain = S)), Card(SetOfAll(instance_param_or_params = sub_expr1, instance_element = Mod(x, L), domain = S))), domain = Real), condition = SubsetEq(S, Real)), InSet(L, Real))

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left\{\forall_{S~|~S \subseteq \mathbb{R}}~\left[\forall_{c \in \mathbb{R}}~\left(|\left\{\left(x + c\right) ~\textup{mod}~ L\right\}_{x \in S}| = |\left\{x ~\textup{mod}~ L\right\}_{x \in S}|\right)\right] \textrm{ if } L \in \mathbb{R}\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Conditional	value: 1 condition: 2
1	Operation	operator: 10 operand: 5
2	Operation	operator: 44 operands: 4
3	ExprTuple	5
4	ExprTuple	47, 24
5	Lambda	parameter: 48 body: 7
6	ExprTuple	48
7	Conditional	value: 8 condition: 9
8	Operation	operator: 10 operand: 14
9	Operation	operator: 12 operands: 13
10	Literal
11	ExprTuple	14
12	Literal
13	ExprTuple	48, 24
14	Lambda	parameter: 52 body: 16
15	ExprTuple	52
16	Conditional	value: 17 condition: 18
17	Operation	operator: 19 operands: 20
18	Operation	operator: 44 operands: 21
19	Literal
20	ExprTuple	22, 23
21	ExprTuple	52, 24
22	Operation	operator: 26 operand: 28
23	Operation	operator: 26 operand: 29
24	Literal
25	ExprTuple	28
26	Literal
27	ExprTuple	29
28	Operation	operator: 31 operand: 33
29	Operation	operator: 31 operand: 34
30	ExprTuple	33
31	Literal
32	ExprTuple	34
33	Lambda	parameter: 51 body: 35
34	Lambda	parameter: 51 body: 37
35	Conditional	value: 38 condition: 40
36	ExprTuple	51
37	Conditional	value: 39 condition: 40
38	Operation	operator: 42 operands: 41
39	Operation	operator: 42 operands: 43
40	Operation	operator: 44 operands: 45
41	ExprTuple	46, 47
42	Literal
43	ExprTuple	51, 47
44	Literal
45	ExprTuple	51, 48
46	Operation	operator: 49 operands: 50
47	Variable
48	Variable
49	Literal
50	ExprTuple	51, 52
51	Variable
52	Variable

Expression of type Conditional¶

from the theory of proveit.numbers.modular¶

Expression of type Conditional ¶

from the theory of proveit.numbers.modular ¶