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, ExprTuple, Lambda, f
from proveit.logic import And, Bijections, Equals, InSet, Injections, Surjections

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(f, Equals(InSet(f, Bijections(A, B)), And(InSet(f, Injections(A, B)), InSet(f, Surjections(A, B)))).with_wrapping_at(2)))

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 \mapsto \left(\begin{array}{c} \begin{array}{l} \left(f \in \left[A \xrightarrow[\text{onto}]{\text{1-to-1}} B\right]\right) =  \\ \left(\left(f \in \left[A \xrightarrow[]{\text{1-to-1}} B\right]\right) \land \left(f \in \left[A \xrightarrow[\text{onto}]{} B\right]\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	parameter: 19 body: 3
2	ExprTuple	19
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 16 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	19, 11
9	Literal
10	ExprTuple	12, 13
11	Operation	operator: 14 operands: 23
12	Operation	operator: 16 operands: 15
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	19, 18
16	Literal
17	ExprTuple	19, 20
18	Operation	operator: 21 operands: 23
19	Variable
20	Operation	operator: 22 operands: 23
21	Literal
22	Literal
23	ExprTuple	24, 25
24	Variable
25	Variable