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, Conditional, ExprTuple, Lambda, f, fx, x
from proveit.logic import InSet, Surjections

# build up the expression from sub-expressions
sub_expr1 = Surjections(A, B)
expr = ExprTuple(Lambda(f, Conditional(InSet(f, sub_expr1), InSet(Lambda(x, Conditional(fx, InSet(x, A))), sub_expr1))))

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\{f \in \left[A \xrightarrow[\text{onto}]{} B\right] \textrm{ if } \left[x \mapsto \left\{f\left(x\right) \textrm{ if } x \in A\right..\right] \in \left[A \xrightarrow[\text{onto}]{} B\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	parameter: 16 body: 3
2	ExprTuple	16
3	Conditional	value: 4 condition: 5
4	Operation	operator: 18 operands: 6
5	Operation	operator: 18 operands: 7
6	ExprTuple	16, 9
7	ExprTuple	8, 9
8	Lambda	parameter: 20 body: 10
9	Operation	operator: 11 operands: 12
10	Conditional	value: 13 condition: 14
11	Literal
12	ExprTuple	21, 15
13	Operation	operator: 16 operand: 20
14	Operation	operator: 18 operands: 19
15	Variable
16	Variable
17	ExprTuple	20
18	Literal
19	ExprTuple	20, 21
20	Variable
21	Variable