Expression of type Forall

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

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [V], instance_expr = 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), domain = 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())

\forall_{V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\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]\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: 18 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 22 body: 4
3	ExprTuple	22
4	Conditional	value: 5 condition: 6
5	Operation	operator: 18 operand: 10
6	Operation	operator: 8 operands: 9
7	ExprTuple	10
8	Literal
9	ExprTuple	22, 11
10	Lambda	parameter: 45 body: 13
11	Operation	operator: 14 operand: 41
12	ExprTuple	45
13	Conditional	value: 16 condition: 17
14	Literal
15	ExprTuple	41
16	Operation	operator: 18 operand: 21
17	Operation	operator: 37 operands: 20
18	Literal
19	ExprTuple	21
20	ExprTuple	45, 22
21	Lambda	parameters: 44 body: 23
22	Variable
23	Conditional	value: 24 condition: 25
24	Operation	operator: 26 operands: 27
25	Operation	operator: 28 operands: 29
26	Literal
27	ExprTuple	30, 31
28	Literal
29	ExprTuple	32, 33
30	Operation	operator: 43 operands: 34
31	Operation	operator: 43 operands: 35
32	Operation	operator: 37 operands: 36
33	Operation	operator: 37 operands: 38
34	ExprTuple	46, 39
35	ExprTuple	40, 45
36	ExprTuple	46, 41
37	Literal
38	ExprTuple	47, 41
39	Operation	operator: 43 operands: 42
40	Operation	operator: 43 operands: 44
41	Variable
42	ExprTuple	47, 45
43	Literal
44	ExprTuple	46, 47
45	Variable
46	Variable
47	Variable