Theorem inner_prod_vec_add_left of type Forall

from the theory of proveit.linear_algebra.inner_products

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.inner_products import inner_prod_vec_add_left

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

Passed sanity check: inner_prod_vec_add_left matches stored_expr

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

\forall_{K}~\left[\forall_{H \underset{{\scriptscriptstyle c}}{\in} \textrm{InnerProdSpaces}\left(K\right)}~\left[\forall_{x, y, z \in H}~\left(\left \langle x + y, z\right \rangle = \left(\left \langle x, z\right \rangle + \left \langle x, z\right \rangle\right)\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: 22 body: 3
3	Operation	operator: 10 operand: 5
4	ExprTuple	5
5	Lambda	parameter: 40 body: 7
6	ExprTuple	40
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	40, 15
14	Lambda	parameters: 16 body: 17
15	Operation	operator: 18 operand: 22
16	ExprTuple	46, 45, 47
17	Conditional	value: 20 condition: 21
18	Literal
19	ExprTuple	22
20	Operation	operator: 23 operands: 24
21	Operation	operator: 25 operands: 26
22	Variable
23	Literal
24	ExprTuple	27, 28
25	Literal
26	ExprTuple	29, 30, 31
27	Operation	operator: 43 operands: 32
28	Operation	operator: 41 operands: 33
29	Operation	operator: 36 operands: 34
30	Operation	operator: 36 operands: 35
31	Operation	operator: 36 operands: 37
32	ExprTuple	38, 47
33	ExprTuple	39, 39
34	ExprTuple	46, 40
35	ExprTuple	45, 40
36	Literal
37	ExprTuple	47, 40
38	Operation	operator: 41 operands: 42
39	Operation	operator: 43 operands: 44
40	Variable
41	Literal
42	ExprTuple	46, 45
43	Literal
44	ExprTuple	46, 47
45	Variable
46	Variable
47	Variable