Expression of type Conditional

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

# build up the expression from sub-expressions
sub_expr1 = Bijections(A, B)
expr = 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 \in \left[A \xrightarrow[\text{onto}]{\text{1-to-1}} 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}]{\text{1-to-1}} B\right]\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 15 operands: 3
2	Operation	operator: 15 operands: 4
3	ExprTuple	13, 6
4	ExprTuple	5, 6
5	Lambda	parameter: 17 body: 7
6	Operation	operator: 8 operands: 9
7	Conditional	value: 10 condition: 11
8	Literal
9	ExprTuple	18, 12
10	Operation	operator: 13 operand: 17
11	Operation	operator: 15 operands: 16
12	Variable
13	Variable
14	ExprTuple	17
15	Literal
16	ExprTuple	17, 18
17	Variable
18	Variable