Expression of type ExprTuple

from the theory of proveit.logic.sets.functions.bijections

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 A, ExprTuple, f, fx, fy, x, y
from proveit.logic import Bijections, Forall, Image, InSet, NotEquals

# build up the expression from sub-expressions
expr = ExprTuple(Forall(instance_param_or_params = [x, y], instance_expr = NotEquals(fx, fy), domain = A, condition = NotEquals(x, y)), InSet(f, Bijections(A, Image(f, A))))

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(\forall_{x, y \in A~|~x \neq y}~\left(f\left(x\right) \neq f\left(y\right)\right), f \in \left[A \xrightarrow[\text{onto}]{\text{1-to-1}} f^{\rightarrow}(A)\right]\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

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