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 A, Conditional, Lambda, X, c
from proveit.linear_algebra import HilbertSpaces, Hspace, LinMap
from proveit.logic import Forall, InSet
from proveit.numbers import Complex
from proveit.physics.quantum import Qmult

# build up the expression from sub-expressions
sub_expr1 = LinMap(Hspace, X)
expr = Lambda(c, Conditional(Forall(instance_param_or_params = [Hspace, X], instance_expr = Forall(instance_param_or_params = [A], instance_expr = InSet(Qmult(c, A), sub_expr1), condition = InSet(Qmult(A), sub_expr1)), domain = HilbertSpaces), InSet(c, Complex)))

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())

c \mapsto \left\{\forall_{\mathcal{H}, X \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}}~\left[\forall_{A~|~\left[A\right] \in \mathcal{L}\left(\mathcal{H}, X\right)}~\left(\left(c \thinspace A\right) \in \mathcal{L}\left(\mathcal{H}, X\right)\right)\right] \textrm{ if } c \in \mathbb{C}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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