Expression of type Conditional

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 Conditional, a, j
from proveit.core_expr_types import B_1_to_j
from proveit.linear_algebra import ScalarMult
from proveit.logic import Equals, Forall, InClass, InSet
from proveit.numbers import Complex, NaturalPos
from proveit.physics.quantum import Qmult, QmultCodomain

# build up the expression from sub-expressions
sub_expr1 = Qmult(B_1_to_j)
expr = Conditional(Forall(instance_param_or_params = [a], instance_expr = Forall(instance_param_or_params = [B_1_to_j], instance_expr = Equals(Qmult(a, B_1_to_j), ScalarMult(a, sub_expr1)).with_wrapping_at(2), condition = InClass(sub_expr1, QmultCodomain)), domain = Complex), InSet(j, NaturalPos))

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())

\left\{\forall_{a \in \mathbb{C}}~\left[\forall_{B_{1}, B_{2}, \ldots, B_{j}~|~\left(B_{1} \thinspace  B_{2} \thinspace  \ldots \thinspace  B_{j}\right) \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}}~\left(\begin{array}{c} \begin{array}{l} \left(a\thinspace B_{1} \thinspace  B_{2} \thinspace  \ldots \thinspace  B_{j}\right) =  \\ \left(a \cdot \left(B_{1} \thinspace  B_{2} \thinspace  \ldots \thinspace  B_{j}\right)\right) \end{array} \end{array}\right)\right] \textrm{ if } j \in \mathbb{N}^+\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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