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, x
from proveit.logic import And, Card, Equals, InSet, SetOfAll
from proveit.numbers import Integer, Interval, Mod, greater_eq, one, subtract, zero

# build up the expression from sub-expressions
sub_expr1 = Interval(a, b)
expr = Lambda([a, b], Conditional(Equals(SetOfAll(instance_param_or_params = [x], instance_element = Mod(x, N), domain = sub_expr1), Interval(zero, subtract(N, one))), And(InSet(a, Integer), InSet(b, 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\right) \mapsto \left\{\left\{x ~\textup{mod}~ N\right\}_{x \in \{a~\ldotp \ldotp~b\}} = \{0~\ldotp \ldotp~N - 1\} \textrm{ if } a \in \mathbb{Z} ,  b \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: 45 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11, 12
8	Operation	operator: 13 operand: 20
9	Operation	operator: 44 operands: 15
10	Operation	operator: 36 operands: 16
11	Operation	operator: 36 operands: 17
12	Operation	operator: 18 operands: 19
13	Literal
14	ExprTuple	20
15	ExprTuple	21, 22
16	ExprTuple	46, 23
17	ExprTuple	47, 23
18	Literal
19	ExprTuple	40, 24
20	Lambda	parameter: 41 body: 26
21	Literal
22	Operation	operator: 27 operands: 28
23	Literal
24	Operation	operator: 29 operand: 42
25	ExprTuple	41
26	Conditional	value: 31 condition: 32
27	Literal
28	ExprTuple	40, 33
29	Literal
30	ExprTuple	42
31	Operation	operator: 34 operands: 35
32	Operation	operator: 36 operands: 37
33	Operation	operator: 38 operand: 43
34	Literal
35	ExprTuple	41, 40
36	Literal
37	ExprTuple	41, 42
38	Literal
39	ExprTuple	43
40	Variable
41	Variable
42	Operation	operator: 44 operands: 45
43	Literal
44	Literal
45	ExprTuple	46, 47
46	Variable
47	Variable