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 Q, f
from proveit.core_expr_types import A_1_to_m, C_1_to_n, Q__b_1_to_j, b_1_to_j, f__b_1_to_j
from proveit.linear_algebra import VecSum
from proveit.linear_algebra.addition import vec_summation_b1toj_fQ
from proveit.logic import Equals, Forall, Implies, InClass
from proveit.physics.quantum import Qmult, QmultCodomain

# build up the expression from sub-expressions
sub_expr1 = Qmult(A_1_to_m, vec_summation_b1toj_fQ, C_1_to_n)
expr = Forall(instance_param_or_params = [A_1_to_m, C_1_to_n, f, Q], instance_expr = Implies(InClass(sub_expr1, QmultCodomain), Equals(sub_expr1, VecSum(index_or_indices = [b_1_to_j], summand = Qmult(A_1_to_m, f__b_1_to_j, C_1_to_n), condition = Q__b_1_to_j)).with_wrapping_at(1)).with_wrapping_at(2))

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