Expression of type And

from the theory of proveit.numbers.summation

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 R, S, gy, n, y
from proveit.logic import And, Card, Equals, SetOfAll

# build up the expression from sub-expressions
expr = And(Equals(SetOfAll(instance_param_or_params = [y], instance_element = gy, domain = S), R), Equals(Card(S), n), Equals(Card(R), 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(\left\{g\left(y\right)\right\}_{y \in S} = R\right) \land \left(|S| = n\right) \land \left(|R| = n\right)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4, 5
3	Operation	operator: 8 operands: 6
4	Operation	operator: 8 operands: 7
5	Operation	operator: 8 operands: 9
6	ExprTuple	10, 20
7	ExprTuple	11, 13
8	Literal
9	ExprTuple	12, 13
10	Operation	operator: 14 operand: 19
11	Operation	operator: 17 operand: 29
12	Operation	operator: 17 operand: 20
13	Variable
14	Literal
15	ExprTuple	19
16	ExprTuple	29
17	Literal
18	ExprTuple	20
19	Lambda	parameter: 28 body: 21
20	Variable
21	Conditional	value: 22 condition: 23
22	Operation	operator: 24 operand: 28
23	Operation	operator: 26 operands: 27
24	Variable
25	ExprTuple	28
26	Literal
27	ExprTuple	28, 29
28	Variable
29	Variable