Expression of type Lambda

from the theory of proveit.physics.quantum

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, alpha, x
from proveit.linear_algebra import ScalarMult
from proveit.logic import Forall, InSet
from proveit.numbers import Complex
from proveit.physics.quantum import QubitSpace

# build up the expression from sub-expressions
expr = Lambda(x, Conditional(Forall(instance_param_or_params = [alpha], instance_expr = InSet(ScalarMult(alpha, x), QubitSpace), domain = Complex), InSet(x, QubitSpace)))

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())

x \mapsto \left\{\forall_{\alpha \in \mathbb{C}}~\left(\left(\alpha \cdot x\right) \in \mathbb{C}^{2}\right) \textrm{ if } x \in \mathbb{C}^{2}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 23 body: 2
1	ExprTuple	23
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 14 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	23, 17
8	Lambda	parameter: 22 body: 10
9	ExprTuple	22
10	Conditional	value: 11 condition: 12
11	Operation	operator: 14 operands: 13
12	Operation	operator: 14 operands: 15
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	22, 24
16	Operation	operator: 18 operands: 19
17	Operation	operator: 20 operands: 21
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	24, 25
22	Variable
23	Variable
24	Literal
25	Literal