Theorem one_as_scalar_mult_id of type Forall

from the theory of proveit.linear_algebra.scalar_multiplication

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.scalar_multiplication import one_as_scalar_mult_id

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

Passed sanity check: one_as_scalar_mult_id matches stored_expr

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

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