Expression of type Conditional

from the theory of proveit.linear_algebra.scalar_multiplication

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, a, b, x, y
from proveit.linear_algebra import binary_lin_comb_ax_by
from proveit.logic import And, Forall, InSet

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [x, y], instance_expr = InSet(binary_lin_comb_ax_by, V), domain = V), And(InSet(a, K), InSet(b, 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, y \in V}~\left(\left(\left(a \cdot x\right) + \left(b \cdot y\right)\right) \in V\right) \textrm{ if } a \in K ,  b \in K\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: 6
2	Operation	operator: 17 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameters: 9 body: 10
7	Operation	operator: 25 operands: 11
8	Operation	operator: 25 operands: 12
9	ExprTuple	34, 36
10	Conditional	value: 13 condition: 14
11	ExprTuple	33, 15
12	ExprTuple	35, 15
13	Operation	operator: 25 operands: 16
14	Operation	operator: 17 operands: 18
15	Variable
16	ExprTuple	19, 29
17	Literal
18	ExprTuple	20, 21
19	Operation	operator: 22 operands: 23
20	Operation	operator: 25 operands: 24
21	Operation	operator: 25 operands: 26
22	Literal
23	ExprTuple	27, 28
24	ExprTuple	34, 29
25	Literal
26	ExprTuple	36, 29
27	Operation	operator: 31 operands: 30
28	Operation	operator: 31 operands: 32
29	Variable
30	ExprTuple	33, 34
31	Literal
32	ExprTuple	35, 36
33	Variable
34	Variable
35	Variable
36	Variable