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, m
from proveit.core_expr_types import A_1_to_m
from proveit.logic import Equals, Forall
from proveit.numbers import NaturalPos
from proveit.physics.quantum import Qmult

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [m], instance_expr = Forall(instance_param_or_params = [A_1_to_m, B], instance_expr = Equals(Qmult(A_1_to_m, B), Qmult(Qmult(A_1_to_m), B)).with_wrapping_at(2)), 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_{m \in \mathbb{N}^+}~\left[\forall_{A_{1}, A_{2}, \ldots, A_{m}, B}~\left(\begin{array}{c} \begin{array}{l} \left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{m} \thinspace B\right) =  \\ \left(\left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{m}\right) \thinspace B\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	parameter: 27 body: 4
3	ExprTuple	27
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	27, 12
11	Lambda	parameters: 18 body: 13
12	Literal
13	Operation	operator: 14 operands: 15
14	Literal
15	ExprTuple	16, 17
16	Operation	operator: 22 operands: 18
17	Operation	operator: 22 operands: 19
18	ExprTuple	24, 21
19	ExprTuple	20, 21
20	Operation	operator: 22 operands: 23
21	Variable
22	Literal
23	ExprTuple	24
24	ExprRange	lambda_map: 25 start_index: 26 end_index: 27
25	Lambda	parameter: 31 body: 28
26	Literal
27	Variable
28	IndexedVar	variable: 29 index: 31
29	Variable
30	ExprTuple	31
31	Variable