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, alpha, beta, x
from proveit.linear_algebra import ScalarMult, VecSpaces
from proveit.logic import Equals, Forall, InClass

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [x], instance_expr = Forall(instance_param_or_params = [alpha, beta], instance_expr = Equals(ScalarMult(alpha, ScalarMult(beta, x)), ScalarMult(ScalarMult(alpha, beta), x)), domain = K), 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[\forall_{\alpha, \beta \in K}~\left(\left(\alpha \cdot \left(\beta \cdot x\right)\right) = \left(\left(\alpha \cdot \beta\right) \cdot x\right)\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: 14 operand: 6
2	Operation	operator: 4 operands: 5
3	ExprTuple	6
4	Literal
5	ExprTuple	18, 7
6	Lambda	parameter: 41 body: 9
7	Operation	operator: 10 operand: 37
8	ExprTuple	41
9	Conditional	value: 12 condition: 13
10	Literal
11	ExprTuple	37
12	Operation	operator: 14 operand: 17
13	Operation	operator: 33 operands: 16
14	Literal
15	ExprTuple	17
16	ExprTuple	41, 18
17	Lambda	parameters: 40 body: 19
18	Variable
19	Conditional	value: 20 condition: 21
20	Operation	operator: 22 operands: 23
21	Operation	operator: 24 operands: 25
22	Literal
23	ExprTuple	26, 27
24	Literal
25	ExprTuple	28, 29
26	Operation	operator: 39 operands: 30
27	Operation	operator: 39 operands: 31
28	Operation	operator: 33 operands: 32
29	Operation	operator: 33 operands: 34
30	ExprTuple	42, 35
31	ExprTuple	36, 41
32	ExprTuple	42, 37
33	Literal
34	ExprTuple	43, 37
35	Operation	operator: 39 operands: 38
36	Operation	operator: 39 operands: 40
37	Variable
38	ExprTuple	43, 41
39	Literal
40	ExprTuple	42, 43
41	Variable
42	Variable
43	Variable