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, Lambda, N, a, b, c, x
from proveit.logic import And, Card, Equals, InSet, SetOfAll
from proveit.numbers import Add, Integer, Interval, Mod, greater_eq

# build up the expression from sub-expressions
sub_expr1 = Interval(a, b)
expr = Lambda([a, b, c], Conditional(Equals(Card(SetOfAll(instance_param_or_params = [x], instance_element = Mod(Add(c, x), N), domain = sub_expr1)), N), And(InSet(a, Integer), InSet(b, Integer), InSet(c, Integer), greater_eq(Card(sub_expr1), N))))

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(a, b, c\right) \mapsto \left\{|\left\{\left(c + x\right) ~\textup{mod}~ N\right\}_{x \in \{a~\ldotp \ldotp~b\}}| = N \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  c \in \mathbb{Z} ,  |\{a~\ldotp \ldotp~b\}| \geq N\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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