Theorem binary_closure of type Forall

from the theory of proveit.linear_algebra.addition

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.linear_algebra.addition import binary_closure

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

Passed sanity check: binary_closure matches stored_expr

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

\forall_{K}~\left[\forall_{V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left[\forall_{x, y \in V}~\left(\left(x + y\right) \in V\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: 10 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 21 body: 3
3	Operation	operator: 10 operand: 5
4	ExprTuple	5
5	Lambda	parameter: 35 body: 7
6	ExprTuple	35
7	Conditional	value: 8 condition: 9
8	Operation	operator: 10 operand: 14
9	Operation	operator: 12 operands: 13
10	Literal
11	ExprTuple	14
12	Literal
13	ExprTuple	35, 15
14	Lambda	parameters: 29 body: 16
15	Operation	operator: 17 operand: 21
16	Conditional	value: 19 condition: 20
17	Literal
18	ExprTuple	21
19	Operation	operator: 31 operands: 22
20	Operation	operator: 23 operands: 24
21	Variable
22	ExprTuple	25, 35
23	Literal
24	ExprTuple	26, 27
25	Operation	operator: 28 operands: 29
26	Operation	operator: 31 operands: 30
27	Operation	operator: 31 operands: 32
28	Literal
29	ExprTuple	33, 34
30	ExprTuple	33, 35
31	Literal
32	ExprTuple	34, 35
33	Variable
34	Variable
35	Variable