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, ExprTuple, f
from proveit.logic import And, Bijections, InSet, Injections, Surjections

# build up the expression from sub-expressions
expr = ExprTuple(InSet(f, Bijections(A, B)), And(InSet(f, Injections(A, B)), InSet(f, Surjections(A, B))))

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], \left(f \in \left[A \xrightarrow[]{\text{1-to-1}} B\right]\right) \land \left(f \in \left[A \xrightarrow[\text{onto}]{} B\right]\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 11 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	14, 6
4	Literal
5	ExprTuple	7, 8
6	Operation	operator: 9 operands: 18
7	Operation	operator: 11 operands: 10
8	Operation	operator: 11 operands: 12
9	Literal
10	ExprTuple	14, 13
11	Literal
12	ExprTuple	14, 15
13	Operation	operator: 16 operands: 18
14	Variable
15	Operation	operator: 17 operands: 18
16	Literal
17	Literal
18	ExprTuple	19, 20
19	Variable
20	Variable