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

# build up the expression from sub-expressions
sub_expr1 = Bijections(A, B)
expr = ExprTuple(Lambda([A, B], Forall(instance_param_or_params = [f], instance_expr = InSet(f, sub_expr1), condition = 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(\left(A, B\right) \mapsto \left[\forall_{f~|~\left[x \mapsto \left\{f\left(x\right) \textrm{ if } x \in A\right..\right] \in \left[A \xrightarrow[\text{onto}]{\text{1-to-1}} B\right]}~\left(f \in \left[A \xrightarrow[\text{onto}]{\text{1-to-1}} B\right]\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: 16 body: 2
2	Operation	operator: 3 operand: 5
3	Literal
4	ExprTuple	5
5	Lambda	parameter: 20 body: 7
6	ExprTuple	20
7	Conditional	value: 8 condition: 9
8	Operation	operator: 22 operands: 10
9	Operation	operator: 22 operands: 11
10	ExprTuple	20, 13
11	ExprTuple	12, 13
12	Lambda	parameter: 24 body: 14
13	Operation	operator: 15 operands: 16
14	Conditional	value: 17 condition: 18
15	Literal
16	ExprTuple	25, 19
17	Operation	operator: 20 operand: 24
18	Operation	operator: 22 operands: 23
19	Variable
20	Variable
21	ExprTuple	24
22	Literal
23	ExprTuple	24, 25
24	Variable
25	Variable