Expression of type Conditional

from the theory of proveit.linear_algebra.tensors

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, Conditional, K, V
from proveit.linear_algebra import TensorProd, VecSpaces
from proveit.logic import Equals, Forall, InClass

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [A], instance_expr = Equals(TensorProd(A), A), domain = V), InClass(V, VecSpaces(K)))

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\{\forall_{A \in V}~\left(\left[{\otimes}\right]\left(A\right) = A\right) \textrm{ if } V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operand: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	20, 8
7	Lambda	parameter: 23 body: 9
8	Operation	operator: 10 operand: 14
9	Conditional	value: 12 condition: 13
10	Literal
11	ExprTuple	14
12	Operation	operator: 15 operands: 16
13	Operation	operator: 17 operands: 18
14	Variable
15	Literal
16	ExprTuple	19, 23
17	Literal
18	ExprTuple	23, 20
19	Operation	operator: 21 operand: 23
20	Variable
21	Literal
22	ExprTuple	23
23	Variable