Expression of type ExprTuple

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

# build up the expression from sub-expressions
expr = ExprTuple(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(\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)\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: 22 body: 2
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 32 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	29, 11
10	Lambda	parameters: 35 body: 12
11	Operation	operator: 13 operands: 14
12	Conditional	value: 15 condition: 16
13	Literal
14	ExprTuple	36, 17
15	Operation	operator: 34 operands: 18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operands: 22
18	ExprTuple	23, 24
19	Literal
20	ExprTuple	25, 26, 27
21	Literal
22	ExprTuple	29, 36
23	Operation	operator: 29 operand: 37
24	Operation	operator: 29 operand: 38
25	Operation	operator: 32 operands: 31
26	Operation	operator: 32 operands: 33
27	Operation	operator: 34 operands: 35
28	ExprTuple	37
29	Variable
30	ExprTuple	38
31	ExprTuple	37, 36
32	Literal
33	ExprTuple	38, 36
34	Literal
35	ExprTuple	37, 38
36	Variable
37	Variable
38	Variable