Theorem membership_folding of type Forall

from the theory of proveit.logic.sets.functions.injections

see dependencies

import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.logic.sets.functions.injections import membership_folding

# check that the built expression is the same as the stored expression
assert membership_folding.expr == stored_expr
assert membership_folding.expr._style_id == stored_expr._style_id
print("Passed sanity check: membership_folding matches stored_expr")

Passed sanity check: membership_folding matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{A, B}~\left[\forall_{f \in \left[A \rightarrow B\right]~|~\forall_{a, b \in A~|~a \neq b}~\left(f\left(a\right) \neq f\left(b\right)\right)}~\left(f \in \left[A \xrightarrow[]{\text{1-to-1}} B\right]\right)\right]

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 17 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 22 body: 3
3	Operation	operator: 17 operand: 5
4	ExprTuple	5
5	Lambda	parameter: 36 body: 7
6	ExprTuple	36
7	Conditional	value: 8 condition: 9
8	Operation	operator: 39 operands: 10
9	Operation	operator: 28 operands: 11
10	ExprTuple	36, 12
11	ExprTuple	13, 14
12	Operation	operator: 15 operands: 22
13	Operation	operator: 39 operands: 16
14	Operation	operator: 17 operand: 20
15	Literal
16	ExprTuple	36, 19
17	Literal
18	ExprTuple	20
19	Operation	operator: 21 operands: 22
20	Lambda	parameters: 42 body: 23
21	Literal
22	ExprTuple	43, 24
23	Conditional	value: 25 condition: 26
24	Variable
25	Operation	operator: 41 operands: 27
26	Operation	operator: 28 operands: 29
27	ExprTuple	30, 31
28	Literal
29	ExprTuple	32, 33, 34
30	Operation	operator: 36 operand: 44
31	Operation	operator: 36 operand: 45
32	Operation	operator: 39 operands: 38
33	Operation	operator: 39 operands: 40
34	Operation	operator: 41 operands: 42
35	ExprTuple	44
36	Variable
37	ExprTuple	45
38	ExprTuple	44, 43
39	Literal
40	ExprTuple	45, 43
41	Literal
42	ExprTuple	44, 45
43	Variable
44	Variable
45	Variable