Expression of type Forall

from the theory of proveit.physics.quantum.QPE

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 t
from proveit.linear_algebra import Norm
from proveit.logic import And, CartExp, Equals, Forall, InSet
from proveit.numbers import Complex, NaturalPos, one
from proveit.physics.quantum.QPE import _psi_t_ket, two_pow_t

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [t], instance_expr = And(InSet(_psi_t_ket, CartExp(Complex, two_pow_t)), Equals(Norm(_psi_t_ket), one)), domain = 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())

\forall_{t \in \mathbb{N}^+}~\left(\left(\lvert \psi_{t} \rangle \in \mathbb{C}^{2^{t}}\right) \land \left(\left \|\lvert \psi_{t} \rangle\right \| = 1\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

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