Expression of type ExprTuple

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, ExprTuple, L, Lambda, S, c, x
from proveit.logic import Card, Equals, Forall, SetOfAll, SubsetEq
from proveit.numbers import Add, Mod, Real

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

expr:

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

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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