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, 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 = And(InSet(f, Functions(A, B)), Forall(instance_param_or_params = [a, b], instance_expr = NotEquals(fa, fb), domain = A, condition = NotEquals(a, b))), domain = 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(\left(A, B\right) \mapsto \left[\forall_{f \in \left[A \xrightarrow[]{\text{1-to-1}} B\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)\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: 21 body: 2
2	Operation	operator: 15 operand: 4
3	ExprTuple	4
4	Lambda	parameter: 35 body: 6
5	ExprTuple	35
6	Conditional	value: 7 condition: 8
7	Operation	operator: 27 operands: 9
8	Operation	operator: 38 operands: 10
9	ExprTuple	11, 12
10	ExprTuple	35, 13
11	Operation	operator: 38 operands: 14
12	Operation	operator: 15 operand: 19
13	Operation	operator: 17 operands: 21
14	ExprTuple	35, 18
15	Literal
16	ExprTuple	19
17	Literal
18	Operation	operator: 20 operands: 21
19	Lambda	parameters: 41 body: 22
20	Literal
21	ExprTuple	42, 23
22	Conditional	value: 24 condition: 25
23	Variable
24	Operation	operator: 40 operands: 26
25	Operation	operator: 27 operands: 28
26	ExprTuple	29, 30
27	Literal
28	ExprTuple	31, 32, 33
29	Operation	operator: 35 operand: 43
30	Operation	operator: 35 operand: 44
31	Operation	operator: 38 operands: 37
32	Operation	operator: 38 operands: 39
33	Operation	operator: 40 operands: 41
34	ExprTuple	43
35	Variable
36	ExprTuple	44
37	ExprTuple	43, 42
38	Literal
39	ExprTuple	44, 42
40	Literal
41	ExprTuple	43, 44
42	Variable
43	Variable
44	Variable