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
from proveit.core_expr_types import A_1_to_l, C_1_to_n
from proveit.logic import Equals, Forall, InClass
from proveit.physics.quantum import Qmult, QmultCodomain

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [A_1_to_l, C_1_to_n], instance_expr = Equals(Qmult(A_1_to_l, b, C_1_to_n), Qmult(b, A_1_to_l, C_1_to_n)).with_wrapping_at(2), condition = InClass(Qmult(A_1_to_l, C_1_to_n), QmultCodomain))

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_{A_{1}, A_{2}, \ldots, A_{l}, C_{1}, C_{2}, \ldots, C_{n}~|~\left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l}\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 b\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) =  \\ \left(b\thinspace A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l}\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) \end{array} \end{array}\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: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 18 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	13, 14
11	Operation	operator: 17 operands: 15
12	Operation	operator: 17 operands: 16
13	Operation	operator: 17 operands: 18
14	Literal
15	ExprTuple	20, 19, 21
16	ExprTuple	19, 20, 21
17	Literal
18	ExprTuple	20, 21
19	Variable
20	ExprRange	lambda_map: 22 start_index: 25 end_index: 23
21	ExprRange	lambda_map: 24 start_index: 25 end_index: 26
22	Lambda	parameter: 32 body: 27
23	Variable
24	Lambda	parameter: 32 body: 28
25	Literal
26	Variable
27	IndexedVar	variable: 29 index: 32
28	IndexedVar	variable: 30 index: 32
29	Variable
30	Variable
31	ExprTuple	32
32	Variable