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

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