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 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
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 = Forall(instance_param_or_params = [j], instance_expr = 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), domain = 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())

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