Expression of type ExprTuple

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

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, Equals, Functions, Image, InSet, Surjections

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(f, Equals(InSet(f, Surjections(A, B)), And(InSet(f, Functions(A, B)), Equals(Image(f, 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}]{} B\right]\right) =  \\ \left(\left(f \in \left[A \rightarrow B\right]\right) \land \left(f^{\rightarrow}(A) = B\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: 25 body: 3
2	ExprTuple	25
3	Operation	operator: 16 operands: 4
4	ExprTuple	5, 6
5	Operation	operator: 14 operands: 7
6	Operation	operator: 8 operands: 9
7	ExprTuple	25, 10
8	Literal
9	ExprTuple	11, 12
10	Operation	operator: 13 operands: 21
11	Operation	operator: 14 operands: 15
12	Operation	operator: 16 operands: 17
13	Literal
14	Literal
15	ExprTuple	25, 18
16	Literal
17	ExprTuple	19, 24
18	Operation	operator: 20 operands: 21
19	Operation	operator: 22 operands: 23
20	Literal
21	ExprTuple	26, 24
22	Literal
23	ExprTuple	25, 26
24	Variable
25	Variable
26	Variable