Expression of type ExprTuple

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

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(m, Conditional(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)), InSet(m, 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(m \mapsto \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) \textrm{ if } m \in \mathbb{N}^+\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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