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 l, m, n
from proveit.core_expr_types import A_1_to_l, B_1_to_m, C_1_to_n
from proveit.logic import Equals, Forall, InClass
from proveit.numbers import Natural, NaturalPos
from proveit.physics.quantum import Qmult, QmultCodomain

# build up the expression from sub-expressions
sub_expr1 = Qmult(A_1_to_l, B_1_to_m, C_1_to_n)
expr = Forall(instance_param_or_params = [l, m, n], instance_expr = Forall(instance_param_or_params = [A_1_to_l, B_1_to_m, C_1_to_n], instance_expr = Equals(sub_expr1, Qmult(A_1_to_l, Qmult(B_1_to_m), C_1_to_n)).with_wrapping_at(2), condition = InClass(sub_expr1, QmultCodomain)), domains = [Natural, NaturalPos, Natural])

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_{l \in \mathbb{N}, m \in \mathbb{N}^+, n \in \mathbb{N}}~\left[\forall_{A_{1}, A_{2}, \ldots, A_{l}, B_{1}, B_{2}, \ldots, B_{m}, C_{1}, C_{2}, \ldots, C_{n}~|~\left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l}\thinspace B_{1} \thinspace  B_{2} \thinspace  \ldots \thinspace  B_{m}\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_{1} \thinspace  B_{2} \thinspace  \ldots \thinspace  B_{m}\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) =  \\ \left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l} \thinspace \left(B_{1} \thinspace  B_{2} \thinspace  \ldots \thinspace  B_{m}\right)\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\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	parameters: 3 body: 4
3	ExprTuple	39, 47, 41
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	12, 13, 14
11	Lambda	parameters: 32 body: 15
12	Operation	operator: 18 operands: 16
13	Operation	operator: 18 operands: 17
14	Operation	operator: 18 operands: 19
15	Conditional	value: 20 condition: 21
16	ExprTuple	39, 23
17	ExprTuple	47, 22
18	Literal
19	ExprTuple	41, 23
20	Operation	operator: 24 operands: 25
21	Operation	operator: 26 operands: 27
22	Literal
23	Literal
24	Literal
25	ExprTuple	29, 28
26	Literal
27	ExprTuple	29, 30
28	Operation	operator: 36 operands: 31
29	Operation	operator: 36 operands: 32
30	Literal
31	ExprTuple	34, 33, 35
32	ExprTuple	34, 42, 35
33	Operation	operator: 36 operands: 37
34	ExprRange	lambda_map: 38 start_index: 46 end_index: 39
35	ExprRange	lambda_map: 40 start_index: 46 end_index: 41
36	Literal
37	ExprTuple	42
38	Lambda	parameter: 53 body: 43
39	Variable
40	Lambda	parameter: 53 body: 44
41	Variable
42	ExprRange	lambda_map: 45 start_index: 46 end_index: 47
43	IndexedVar	variable: 48 index: 53
44	IndexedVar	variable: 49 index: 53
45	Lambda	parameter: 53 body: 50
46	Literal
47	Variable
48	Variable
49	Variable
50	IndexedVar	variable: 51 index: 53
51	Variable
52	ExprTuple	53
53	Variable