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, Implies, InSet

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([f, g, A, B, C], Implies(And(InSet(f, Bijections(A, B)), InSet(g, Bijections(B, C))), InSet(Lambda(x, Conditional(Function(g, [fx]), InSet(x, A))), Bijections(A, C))).with_wrapping_at(1)))

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, g, A, B, C\right) \mapsto \left(\begin{array}{c} \begin{array}{l} \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)\right) \\  \Rightarrow \left(\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) \end{array} \end{array}\right)\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	34, 26, 33, 30, 31
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 28 operands: 10
8	Literal
9	ExprTuple	11, 12
10	ExprTuple	13, 14
11	Operation	operator: 28 operands: 15
12	Operation	operator: 28 operands: 16
13	Lambda	parameter: 36 body: 17
14	Operation	operator: 24 operands: 18
15	ExprTuple	34, 19
16	ExprTuple	26, 20
17	Conditional	value: 21 condition: 22
18	ExprTuple	33, 31
19	Operation	operator: 24 operands: 23
20	Operation	operator: 24 operands: 25
21	Operation	operator: 26 operand: 32
22	Operation	operator: 28 operands: 29
23	ExprTuple	33, 30
24	Literal
25	ExprTuple	30, 31
26	Variable
27	ExprTuple	32
28	Literal
29	ExprTuple	36, 33
30	Variable
31	Variable
32	Operation	operator: 34 operand: 36
33	Variable
34	Variable
35	ExprTuple	36
36	Variable