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.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
from proveit.physics.quantum import Qmult, QmultCodomain

# build up the expression from sub-expressions
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)

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_{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]

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: 6 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 35 body: 3
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	11
10	Lambda	parameters: 31 body: 12
11	ExprRange	lambda_map: 13 start_index: 41 end_index: 42
12	Conditional	value: 14 condition: 15
13	Lambda	parameter: 47 body: 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operands: 20
16	Operation	operator: 21 operands: 22
17	Literal
18	ExprTuple	23, 24
19	Literal
20	ExprTuple	25, 26
21	Literal
22	ExprTuple	44, 27
23	Operation	operator: 30 operands: 28
24	Operation	operator: 30 operands: 29
25	Operation	operator: 30 operands: 31
26	Literal
27	Literal
28	ExprTuple	38, 33
29	ExprTuple	32, 33
30	Literal
31	ExprTuple	33
32	Operation	operator: 34 operands: 35
33	ExprRange	lambda_map: 36 start_index: 41 end_index: 37
34	Literal
35	ExprTuple	38
36	Lambda	parameter: 47 body: 39
37	Variable
38	ExprRange	lambda_map: 40 start_index: 41 end_index: 42
39	IndexedVar	variable: 43 index: 47
40	Lambda	parameter: 47 body: 44
41	Literal
42	Variable
43	Variable
44	IndexedVar	variable: 45 index: 47
45	Variable
46	ExprTuple	47
47	Variable