Expression of type Forall

from the theory of proveit.linear_algebra.linear_maps

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, B, Composition, K, V
from proveit.linear_algebra import Commutator, VecAdd, VecNeg, VecSpaces
from proveit.logic import Equals, Forall

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [K], instance_expr = Forall(instance_param_or_params = [V], instance_expr = Forall(instance_param_or_params = [A, B], instance_expr = Equals(Commutator(A, B), VecAdd(Composition(A, B), VecNeg(Composition(B, A)))), 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_{K}~\left[\forall_{V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left[\forall_{A, B \in V}~\left(\left[A, B\right] = \left(\left(A \circ B\right) + \left(-\left(B \circ A\right)\right)\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: 10 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 21 body: 3
3	Operation	operator: 10 operand: 5
4	ExprTuple	5
5	Lambda	parameter: 38 body: 7
6	ExprTuple	38
7	Conditional	value: 8 condition: 9
8	Operation	operator: 10 operand: 14
9	Operation	operator: 12 operands: 13
10	Literal
11	ExprTuple	14
12	Literal
13	ExprTuple	38, 15
14	Lambda	parameters: 39 body: 16
15	Operation	operator: 17 operand: 21
16	Conditional	value: 19 condition: 20
17	Literal
18	ExprTuple	21
19	Operation	operator: 22 operands: 23
20	Operation	operator: 24 operands: 25
21	Variable
22	Literal
23	ExprTuple	26, 27
24	Literal
25	ExprTuple	28, 29
26	Operation	operator: 30 operands: 39
27	Operation	operator: 31 operands: 32
28	Operation	operator: 34 operands: 33
29	Operation	operator: 34 operands: 35
30	Literal
31	Literal
32	ExprTuple	36, 37
33	ExprTuple	46, 38
34	Literal
35	ExprTuple	45, 38
36	Operation	operator: 43 operands: 39
37	Operation	operator: 40 operand: 42
38	Variable
39	ExprTuple	46, 45
40	Literal
41	ExprTuple	42
42	Operation	operator: 43 operands: 44
43	Literal
44	ExprTuple	45, 46
45	Variable
46	Variable