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, InSet, SetOfAll, SubsetEq
from proveit.numbers import Add, Mod, Real

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = ExprTuple(Lambda(L, 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))))

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(L \mapsto \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..\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: 50 body: 3
2	ExprTuple	50
3	Conditional	value: 4 condition: 5
4	Operation	operator: 13 operand: 8
5	Operation	operator: 47 operands: 7
6	ExprTuple	8
7	ExprTuple	50, 27
8	Lambda	parameter: 51 body: 10
9	ExprTuple	51
10	Conditional	value: 11 condition: 12
11	Operation	operator: 13 operand: 17
12	Operation	operator: 15 operands: 16
13	Literal
14	ExprTuple	17
15	Literal
16	ExprTuple	51, 27
17	Lambda	parameter: 55 body: 19
18	ExprTuple	55
19	Conditional	value: 20 condition: 21
20	Operation	operator: 22 operands: 23
21	Operation	operator: 47 operands: 24
22	Literal
23	ExprTuple	25, 26
24	ExprTuple	55, 27
25	Operation	operator: 29 operand: 31
26	Operation	operator: 29 operand: 32
27	Literal
28	ExprTuple	31
29	Literal
30	ExprTuple	32
31	Operation	operator: 34 operand: 36
32	Operation	operator: 34 operand: 37
33	ExprTuple	36
34	Literal
35	ExprTuple	37
36	Lambda	parameter: 54 body: 38
37	Lambda	parameter: 54 body: 40
38	Conditional	value: 41 condition: 43
39	ExprTuple	54
40	Conditional	value: 42 condition: 43
41	Operation	operator: 45 operands: 44
42	Operation	operator: 45 operands: 46
43	Operation	operator: 47 operands: 48
44	ExprTuple	49, 50
45	Literal
46	ExprTuple	54, 50
47	Literal
48	ExprTuple	54, 51
49	Operation	operator: 52 operands: 53
50	Variable
51	Variable
52	Literal
53	ExprTuple	54, 55
54	Variable
55	Variable