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, Forall, Functions, Image, InSet, Surjections

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([A, B], Forall(instance_param_or_params = [f], instance_expr = 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(\left(A, B\right) \mapsto \left[\forall_{f}~\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]\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: 25 body: 2
2	Operation	operator: 3 operand: 5
3	Literal
4	ExprTuple	5
5	Lambda	parameter: 29 body: 7
6	ExprTuple	29
7	Operation	operator: 20 operands: 8
8	ExprTuple	9, 10
9	Operation	operator: 18 operands: 11
10	Operation	operator: 12 operands: 13
11	ExprTuple	29, 14
12	Literal
13	ExprTuple	15, 16
14	Operation	operator: 17 operands: 25
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Literal
18	Literal
19	ExprTuple	29, 22
20	Literal
21	ExprTuple	23, 28
22	Operation	operator: 24 operands: 25
23	Operation	operator: 26 operands: 27
24	Literal
25	ExprTuple	30, 28
26	Literal
27	ExprTuple	29, 30
28	Variable
29	Variable
30	Variable