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 A, Conditional, ExprTuple, 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 = ExprTuple(Lambda(c, Conditional(Forall(instance_param_or_params = [Hspace, X], instance_expr = Forall(instance_param_or_params = [A], instance_expr = InSet(Qmult(A, c), 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())

\left(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(A \thinspace c\right) \in \mathcal{L}\left(\mathcal{H}, X\right)\right)\right] \textrm{ if } c \in \mathbb{C}\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: 38 body: 3
2	ExprTuple	38
3	Conditional	value: 4 condition: 5
4	Operation	operator: 13 operand: 8
5	Operation	operator: 28 operands: 7
6	ExprTuple	8
7	ExprTuple	38, 9
8	Lambda	parameters: 37 body: 10
9	Literal
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	18, 19
17	Lambda	parameter: 39 body: 20
18	Operation	operator: 22 operands: 21
19	Operation	operator: 22 operands: 23
20	Conditional	value: 24 condition: 25
21	ExprTuple	40, 26
22	Literal
23	ExprTuple	41, 26
24	Operation	operator: 28 operands: 27
25	Operation	operator: 28 operands: 29
26	Literal
27	ExprTuple	30, 32
28	Literal
29	ExprTuple	31, 32
30	Operation	operator: 34 operands: 33
31	Operation	operator: 34 operand: 39
32	Operation	operator: 36 operands: 37
33	ExprTuple	39, 38
34	Literal
35	ExprTuple	39
36	Literal
37	ExprTuple	40, 41
38	Variable
39	Variable
40	Variable
41	Variable