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 B, alpha, l, n
from proveit.core_expr_types import A_1_to_l, C_1_to_n
from proveit.linear_algebra import ScalarMult
from proveit.logic import Equals, Forall, InClass
from proveit.numbers import Complex, Natural
from proveit.physics.quantum import Qmult, QmultCodomain

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [alpha, l, n], instance_expr = Forall(instance_param_or_params = [A_1_to_l, B, C_1_to_n], instance_expr = Equals(Qmult(A_1_to_l, ScalarMult(alpha, B), C_1_to_n), Qmult(A_1_to_l, alpha, B, C_1_to_n)).with_wrapping_at(2), condition = InClass(Qmult(A_1_to_l, B, C_1_to_n), QmultCodomain)), domains = [Complex, Natural, 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_{\alpha \in \mathbb{C}, l \in \mathbb{N}, n \in \mathbb{N}}~\left[\forall_{A_{1}, A_{2}, \ldots, A_{l}, B, C_{1}, C_{2}, \ldots, C_{n}~|~\left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l} \thinspace B\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}}~\left(\begin{array}{c} \begin{array}{l} \left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l} \thinspace \left(\alpha \cdot B\right)\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) =  \\ \left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l} \thinspace \alpha \thinspace B\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\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: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 3 body: 4
3	ExprTuple	46, 42, 45
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 11
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11
9	Literal
10	ExprTuple	12, 13, 14
11	Lambda	parameters: 35 body: 15
12	Operation	operator: 18 operands: 16
13	Operation	operator: 18 operands: 17
14	Operation	operator: 18 operands: 19
15	Conditional	value: 20 condition: 21
16	ExprTuple	46, 22
17	ExprTuple	42, 23
18	Literal
19	ExprTuple	45, 23
20	Operation	operator: 24 operands: 25
21	Operation	operator: 26 operands: 27
22	Literal
23	Literal
24	Literal
25	ExprTuple	28, 29
26	Literal
27	ExprTuple	30, 31
28	Operation	operator: 34 operands: 32
29	Operation	operator: 34 operands: 33
30	Operation	operator: 34 operands: 35
31	Literal
32	ExprTuple	37, 36, 38
33	ExprTuple	37, 46, 47, 38
34	Literal
35	ExprTuple	37, 47, 38
36	Operation	operator: 39 operands: 40
37	ExprRange	lambda_map: 41 start_index: 44 end_index: 42
38	ExprRange	lambda_map: 43 start_index: 44 end_index: 45
39	Literal
40	ExprTuple	46, 47
41	Lambda	parameter: 53 body: 48
42	Variable
43	Lambda	parameter: 53 body: 49
44	Literal
45	Variable
46	Variable
47	Variable
48	IndexedVar	variable: 50 index: 53
49	IndexedVar	variable: 51 index: 53
50	Variable
51	Variable
52	ExprTuple	53
53	Variable