Expression of type ExprTuple

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

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, B, ExprTuple, a, b, f, fa, fb
from proveit.logic import And, Forall, Functions, InSet, Injections, NotEquals

# build up the expression from sub-expressions
expr = ExprTuple(InSet(f, Injections(A, B)), And(InSet(f, Functions(A, B)), Forall(instance_param_or_params = [a, b], instance_expr = NotEquals(fa, fb), domain = A, condition = NotEquals(a, b))))

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(f \in \left[A \xrightarrow[]{\text{1-to-1}} B\right], \left(f \in \left[A \rightarrow B\right]\right) \land \left[\forall_{a, b \in A~|~a \neq b}~\left(f\left(a\right) \neq f\left(b\right)\right)\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: 32 operands: 3
2	Operation	operator: 21 operands: 4
3	ExprTuple	29, 5
4	ExprTuple	6, 7
5	Operation	operator: 8 operands: 15
6	Operation	operator: 32 operands: 9
7	Operation	operator: 10 operand: 13
8	Literal
9	ExprTuple	29, 12
10	Literal
11	ExprTuple	13
12	Operation	operator: 14 operands: 15
13	Lambda	parameters: 35 body: 16
14	Literal
15	ExprTuple	36, 17
16	Conditional	value: 18 condition: 19
17	Variable
18	Operation	operator: 34 operands: 20
19	Operation	operator: 21 operands: 22
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	25, 26, 27
23	Operation	operator: 29 operand: 37
24	Operation	operator: 29 operand: 38
25	Operation	operator: 32 operands: 31
26	Operation	operator: 32 operands: 33
27	Operation	operator: 34 operands: 35
28	ExprTuple	37
29	Variable
30	ExprTuple	38
31	ExprTuple	37, 36
32	Literal
33	ExprTuple	38, 36
34	Literal
35	ExprTuple	37, 38
36	Variable
37	Variable
38	Variable