Expression of type Lambda

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, 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 = Lambda(f, 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())

f \mapsto \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)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 33 body: 2
1	ExprTuple	33
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 6
5	Operation	operator: 36 operands: 7
6	Operation	operator: 25 operands: 8
7	ExprTuple	33, 9
8	ExprTuple	10, 11
9	Operation	operator: 12 operands: 19
10	Operation	operator: 36 operands: 13
11	Operation	operator: 14 operand: 17
12	Literal
13	ExprTuple	33, 16
14	Literal
15	ExprTuple	17
16	Operation	operator: 18 operands: 19
17	Lambda	parameters: 39 body: 20
18	Literal
19	ExprTuple	40, 21
20	Conditional	value: 22 condition: 23
21	Variable
22	Operation	operator: 38 operands: 24
23	Operation	operator: 25 operands: 26
24	ExprTuple	27, 28
25	Literal
26	ExprTuple	29, 30, 31
27	Operation	operator: 33 operand: 41
28	Operation	operator: 33 operand: 42
29	Operation	operator: 36 operands: 35
30	Operation	operator: 36 operands: 37
31	Operation	operator: 38 operands: 39
32	ExprTuple	41
33	Variable
34	ExprTuple	42
35	ExprTuple	41, 40
36	Literal
37	ExprTuple	42, 40
38	Literal
39	ExprTuple	41, 42
40	Variable
41	Variable
42	Variable