Expression of type Lambda

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, 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 = 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())

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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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