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

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(f, Conditional(And(InSet(f, Functions(A, B)), Forall(instance_param_or_params = [a, b], instance_expr = NotEquals(fa, fb), domain = A, condition = NotEquals(a, b))), InSet(f, Injections(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 \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] \textrm{ if } f \in \left[A \xrightarrow[]{\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: 32 body: 3
2	ExprTuple	32
3	Conditional	value: 4 condition: 5
4	Operation	operator: 24 operands: 6
5	Operation	operator: 35 operands: 7
6	ExprTuple	8, 9
7	ExprTuple	32, 10
8	Operation	operator: 35 operands: 11
9	Operation	operator: 12 operand: 16
10	Operation	operator: 14 operands: 18
11	ExprTuple	32, 15
12	Literal
13	ExprTuple	16
14	Literal
15	Operation	operator: 17 operands: 18
16	Lambda	parameters: 38 body: 19
17	Literal
18	ExprTuple	39, 20
19	Conditional	value: 21 condition: 22
20	Variable
21	Operation	operator: 37 operands: 23
22	Operation	operator: 24 operands: 25
23	ExprTuple	26, 27
24	Literal
25	ExprTuple	28, 29, 30
26	Operation	operator: 32 operand: 40
27	Operation	operator: 32 operand: 41
28	Operation	operator: 35 operands: 34
29	Operation	operator: 35 operands: 36
30	Operation	operator: 37 operands: 38
31	ExprTuple	40
32	Variable
33	ExprTuple	41
34	ExprTuple	40, 39
35	Literal
36	ExprTuple	41, 39
37	Literal
38	ExprTuple	40, 41
39	Variable
40	Variable
41	Variable