Expression of type Lambda

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, Lambda, f, fx, fy, x, y
from proveit.logic import Bijections, Forall, Image, Implies, InSet, NotEquals

# build up the expression from sub-expressions
expr = Lambda([f, A], Implies(Forall(instance_param_or_params = [x, y], instance_expr = NotEquals(fx, fy), domain = A, condition = NotEquals(x, y)), InSet(f, Bijections(A, Image(f, A)))))

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, A\right) \mapsto \left(\left[\forall_{x, y \in A~|~x \neq y}~\left(f\left(x\right) \neq f\left(y\right)\right)\right] \Rightarrow \left(f \in \left[A \xrightarrow[\text{onto}]{\text{1-to-1}} f^{\rightarrow}(A)\right]\right)\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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