Expression of type Lambda

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, Function, Lambda, f, fx, g, x
from proveit.logic import And, Bijections, Implies, InSet

# build up the expression from sub-expressions
expr = 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(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)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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