Expression of type Lambda

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, Lambda, 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 = Lambda(j, 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())

j \mapsto \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()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 39 body: 2
1	ExprTuple	39
2	Conditional	value: 3 condition: 4
3	Operation	operator: 13 operand: 7
4	Operation	operator: 15 operands: 6
5	ExprTuple	7
6	ExprTuple	39, 8
7	Lambda	parameter: 32 body: 10
8	Literal
9	ExprTuple	32
10	Conditional	value: 11 condition: 12
11	Operation	operator: 13 operand: 17
12	Operation	operator: 15 operands: 16
13	Literal
14	ExprTuple	17
15	Literal
16	ExprTuple	32, 18
17	Lambda	parameters: 35 body: 19
18	Literal
19	Conditional	value: 20 condition: 21
20	Operation	operator: 22 operands: 23
21	Operation	operator: 24 operands: 25
22	Literal
23	ExprTuple	26, 27
24	Literal
25	ExprTuple	33, 28
26	Operation	operator: 34 operands: 29
27	Operation	operator: 30 operands: 31
28	Literal
29	ExprTuple	32, 36
30	Literal
31	ExprTuple	32, 33
32	Variable
33	Operation	operator: 34 operands: 35
34	Literal
35	ExprTuple	36
36	ExprRange	lambda_map: 37 start_index: 38 end_index: 39
37	Lambda	parameter: 43 body: 40
38	Literal
39	Variable
40	IndexedVar	variable: 41 index: 43
41	Variable
42	ExprTuple	43
43	Variable