Expression of type Conditional

from the theory of proveit.linear_algebra.addition

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 Conditional, K, V, x
from proveit.linear_algebra import VecAdd, VecSpaces, VecZero
from proveit.logic import Equals, Forall, InClass

# build up the expression from sub-expressions
sub_expr1 = VecZero(V)
expr = Conditional(Forall(instance_param_or_params = [x], instance_expr = Equals(VecAdd(sub_expr1, x), sub_expr1), 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_{x \in V}~\left(\left(\vec{0}\left(V\right) + x\right) = \vec{0}\left(V\right)\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	27, 8
7	Lambda	parameter: 24 body: 10
8	Operation	operator: 11 operand: 15
9	ExprTuple	24
10	Conditional	value: 13 condition: 14
11	Literal
12	ExprTuple	15
13	Operation	operator: 16 operands: 17
14	Operation	operator: 18 operands: 19
15	Variable
16	Literal
17	ExprTuple	20, 23
18	Literal
19	ExprTuple	24, 27
20	Operation	operator: 21 operands: 22
21	Literal
22	ExprTuple	23, 24
23	Operation	operator: 25 operand: 27
24	Variable
25	Literal
26	ExprTuple	27
27	Variable