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 k, t
from proveit.linear_algebra import TensorProd
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Interval, one, subtract, zero
from proveit.physics.quantum import NumKet, ket0
from proveit.physics.quantum.QPE import two_pow_t

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [k], instance_expr = Equals(NumKet(k, Add(t, one)), TensorProd(ket0, NumKet(k, t))), domain = Interval(zero, subtract(two_pow_t, one)))

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_{k \in \{0~\ldotp \ldotp~2^{t} - 1\}}~\left(\lvert k \rangle_{t + 1} = \left(\lvert 0 \rangle {\otimes} \lvert k \rangle_{t}\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: 5
4	ExprTuple	32
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12, 13
10	Literal
11	ExprTuple	32, 14
12	Operation	operator: 27 operands: 15
13	Operation	operator: 16 operands: 17
14	Operation	operator: 18 operands: 19
15	ExprTuple	32, 20
16	Literal
17	ExprTuple	21, 22
18	Literal
19	ExprTuple	31, 23
20	Operation	operator: 29 operands: 24
21	Operation	operator: 25 operand: 31
22	Operation	operator: 27 operands: 28
23	Operation	operator: 29 operands: 30
24	ExprTuple	40, 41
25	Literal
26	ExprTuple	31
27	Literal
28	ExprTuple	32, 40
29	Literal
30	ExprTuple	33, 34
31	Literal
32	Variable
33	Operation	operator: 35 operands: 36
34	Operation	operator: 37 operand: 41
35	Literal
36	ExprTuple	39, 40
37	Literal
38	ExprTuple	41
39	Literal
40	Variable
41	Literal