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, c
from proveit.linear_algebra import HilbertSpaces, Hspace
from proveit.logic import Forall, InSet
from proveit.numbers import Complex
from proveit.physics.quantum import Qmult, var_ket_psi

# build up the expression from sub-expressions
expr = Lambda(c, Conditional(Forall(instance_param_or_params = [Hspace], instance_expr = Forall(instance_param_or_params = [var_ket_psi], instance_expr = InSet(Qmult(c, var_ket_psi), Hspace), domain = Hspace), 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} \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}}~\left[\forall_{\lvert \psi \rangle \in \mathcal{H}}~\left(\left(c \thinspace \lvert \psi \rangle\right) \in \mathcal{H}\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: 30 body: 2
1	ExprTuple	30
2	Conditional	value: 3 condition: 4
3	Operation	operator: 13 operand: 7
4	Operation	operator: 24 operands: 6
5	ExprTuple	7
6	ExprTuple	30, 8
7	Lambda	parameter: 27 body: 10
8	Literal
9	ExprTuple	27
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	27, 18
17	Lambda	parameter: 31 body: 20
18	Literal
19	ExprTuple	31
20	Conditional	value: 21 condition: 22
21	Operation	operator: 24 operands: 23
22	Operation	operator: 24 operands: 25
23	ExprTuple	26, 27
24	Literal
25	ExprTuple	31, 27
26	Operation	operator: 28 operands: 29
27	Variable
28	Literal
29	ExprTuple	30, 31
30	Variable
31	Variable