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, B, C, Conditional, ExprTuple, Function, Lambda, f, fx, g, x
from proveit.logic import And, Bijections, InSet

# build up the expression from sub-expressions
expr = ExprTuple(And(InSet(f, Bijections(A, B)), InSet(g, Bijections(B, C))), InSet(Lambda(x, Conditional(Function(g, [fx]), InSet(x, A))), Bijections(A, C)))

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(f \in \left[A \xrightarrow[\text{onto}]{\text{1-to-1}} B\right]\right) \land \left(g \in \left[B \xrightarrow[\text{onto}]{\text{1-to-1}} C\right]\right), \left[x \mapsto \left\{g\left(f\left(x\right)\right) \textrm{ if } x \in A\right..\right] \in \left[A \xrightarrow[\text{onto}]{\text{1-to-1}} C\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 operands: 4
2	Operation	operator: 23 operands: 5
3	Literal
4	ExprTuple	6, 7
5	ExprTuple	8, 9
6	Operation	operator: 23 operands: 10
7	Operation	operator: 23 operands: 11
8	Lambda	parameter: 31 body: 12
9	Operation	operator: 19 operands: 13
10	ExprTuple	29, 14
11	ExprTuple	21, 15
12	Conditional	value: 16 condition: 17
13	ExprTuple	28, 26
14	Operation	operator: 19 operands: 18
15	Operation	operator: 19 operands: 20
16	Operation	operator: 21 operand: 27
17	Operation	operator: 23 operands: 24
18	ExprTuple	28, 25
19	Literal
20	ExprTuple	25, 26
21	Variable
22	ExprTuple	27
23	Literal
24	ExprTuple	31, 28
25	Variable
26	Variable
27	Operation	operator: 29 operand: 31
28	Variable
29	Variable
30	ExprTuple	31
31	Variable