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

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([A, B], Forall(instance_param_or_params = [f], instance_expr = And(InSet(f, Injections(A, B)), InSet(f, Surjections(A, B))), domain = 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(\left(A, B\right) \mapsto \left[\forall_{f \in \left[A \xrightarrow[\text{onto}]{\text{1-to-1}} B\right]}~\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)\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: 25 body: 2
2	Operation	operator: 3 operand: 5
3	Literal
4	ExprTuple	5
5	Lambda	parameter: 21 body: 7
6	ExprTuple	21
7	Conditional	value: 8 condition: 9
8	Operation	operator: 10 operands: 11
9	Operation	operator: 17 operands: 12
10	Literal
11	ExprTuple	13, 14
12	ExprTuple	21, 15
13	Operation	operator: 17 operands: 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operands: 25
16	ExprTuple	21, 20
17	Literal
18	ExprTuple	21, 22
19	Literal
20	Operation	operator: 23 operands: 25
21	Variable
22	Operation	operator: 24 operands: 25
23	Literal
24	Literal
25	ExprTuple	26, 27
26	Variable
27	Variable