Expression of type Forall

from the theory of proveit.physics.quantum.algebra

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 j, l
from proveit.core_expr_types import A_1_to_l, b_1_to_j
from proveit.logic import Equals, Forall, InClass
from proveit.numbers import Complex, Mult, Natural, NaturalPos
from proveit.physics.quantum import Qmult, QmultCodomain

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [j, l], instance_expr = Forall(instance_param_or_params = [b_1_to_j], instance_expr = Forall(instance_param_or_params = [A_1_to_l], instance_expr = Equals(Qmult(b_1_to_j, A_1_to_l), Qmult(Mult(b_1_to_j), A_1_to_l)).with_wrapping_at(2), condition = InClass(Qmult(A_1_to_l), QmultCodomain)), domain = Complex), domains = [NaturalPos, Natural])

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_{j \in \mathbb{N}^+, l \in \mathbb{N}}~\left[\forall_{b_{1}, b_{2}, \ldots, b_{j} \in \mathbb{C}}~\left[\forall_{A_{1}, A_{2}, \ldots, A_{l}~|~\left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l}\right) \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}}~\left(\begin{array}{c} \begin{array}{l} \left(b_{1} \thinspace  b_{2} \thinspace  \ldots \thinspace  b_{j}\thinspace A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l}\right) =  \\ \left(\left(b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{j}\right)\thinspace A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l}\right) \end{array} \end{array}\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: 19 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 3 body: 4
3	ExprTuple	55, 50
4	Conditional	value: 5 condition: 6
5	Operation	operator: 19 operand: 9
6	Operation	operator: 21 operands: 8
7	ExprTuple	9
8	ExprTuple	10, 11
9	Lambda	parameters: 48 body: 12
10	Operation	operator: 34 operands: 13
11	Operation	operator: 34 operands: 14
12	Conditional	value: 15 condition: 16
13	ExprTuple	55, 17
14	ExprTuple	50, 18
15	Operation	operator: 19 operand: 23
16	Operation	operator: 21 operands: 22
17	Literal
18	Literal
19	Literal
20	ExprTuple	23
21	Literal
22	ExprTuple	24
23	Lambda	parameters: 44 body: 25
24	ExprRange	lambda_map: 26 start_index: 54 end_index: 55
25	Conditional	value: 27 condition: 28
26	Lambda	parameter: 60 body: 29
27	Operation	operator: 30 operands: 31
28	Operation	operator: 32 operands: 33
29	Operation	operator: 34 operands: 35
30	Literal
31	ExprTuple	36, 37
32	Literal
33	ExprTuple	38, 39
34	Literal
35	ExprTuple	57, 40
36	Operation	operator: 43 operands: 41
37	Operation	operator: 43 operands: 42
38	Operation	operator: 43 operands: 44
39	Literal
40	Literal
41	ExprTuple	51, 46
42	ExprTuple	45, 46
43	Literal
44	ExprTuple	46
45	Operation	operator: 47 operands: 48
46	ExprRange	lambda_map: 49 start_index: 54 end_index: 50
47	Literal
48	ExprTuple	51
49	Lambda	parameter: 60 body: 52
50	Variable
51	ExprRange	lambda_map: 53 start_index: 54 end_index: 55
52	IndexedVar	variable: 56 index: 60
53	Lambda	parameter: 60 body: 57
54	Literal
55	Variable
56	Variable
57	IndexedVar	variable: 58 index: 60
58	Variable
59	ExprTuple	60
60	Variable