Expression of type ExprTuple

from the theory of proveit.logic.sets.functions.injections

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, a, b, f, fa, fb
from proveit.logic import And, Equals, Forall, Functions, InSet, Injections, NotEquals

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([A, B], Forall(instance_param_or_params = [f], instance_expr = Equals(InSet(f, Injections(A, B)), And(InSet(f, Functions(A, B)), Forall(instance_param_or_params = [a, b], instance_expr = NotEquals(fa, fb), domain = A, condition = NotEquals(a, b)))).with_wrapping_at(2))))

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(\begin{array}{c} \begin{array}{l} \left(f \in \left[A \xrightarrow[]{\text{1-to-1}} B\right]\right) =  \\ \left(\left(f \in \left[A \rightarrow B\right]\right) \land \left[\forall_{a, b \in A~|~a \neq b}~\left(f\left(a\right) \neq f\left(b\right)\right)\right]\right) \end{array} \end{array}\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: 23 body: 2
2	Operation	operator: 18 operand: 4
3	ExprTuple	4
4	Lambda	parameter: 37 body: 6
5	ExprTuple	37
6	Operation	operator: 7 operands: 8
7	Literal
8	ExprTuple	9, 10
9	Operation	operator: 40 operands: 11
10	Operation	operator: 29 operands: 12
11	ExprTuple	37, 13
12	ExprTuple	14, 15
13	Operation	operator: 16 operands: 23
14	Operation	operator: 40 operands: 17
15	Operation	operator: 18 operand: 21
16	Literal
17	ExprTuple	37, 20
18	Literal
19	ExprTuple	21
20	Operation	operator: 22 operands: 23
21	Lambda	parameters: 43 body: 24
22	Literal
23	ExprTuple	44, 25
24	Conditional	value: 26 condition: 27
25	Variable
26	Operation	operator: 42 operands: 28
27	Operation	operator: 29 operands: 30
28	ExprTuple	31, 32
29	Literal
30	ExprTuple	33, 34, 35
31	Operation	operator: 37 operand: 45
32	Operation	operator: 37 operand: 46
33	Operation	operator: 40 operands: 39
34	Operation	operator: 40 operands: 41
35	Operation	operator: 42 operands: 43
36	ExprTuple	45
37	Variable
38	ExprTuple	46
39	ExprTuple	45, 44
40	Literal
41	ExprTuple	46, 44
42	Literal
43	ExprTuple	45, 46
44	Variable
45	Variable
46	Variable