Expression of type InSet

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 m
from proveit.linear_algebra import LinMap
from proveit.logic import CartExp, InSet
from proveit.numbers import Complex
from proveit.physics.quantum import NumBra, Qmult
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import _t, _two_pow_t

# build up the expression from sub-expressions
expr = InSet(Qmult(Qmult(NumBra(m, _t), InverseFourierTransform(_t))), LinMap(CartExp(Complex, _two_pow_t), 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[{_{t}}\langle m \rvert \thinspace {\mathrm {FT}}^{\dag}_{t}\right] \in \mathcal{L}\left(\mathbb{C}^{2^{t}}, \mathbb{C}\right)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 10 operand: 8
4	Operation	operator: 6 operands: 7
5	ExprTuple	8
6	Literal
7	ExprTuple	9, 16
8	Operation	operator: 10 operands: 11
9	Operation	operator: 12 operands: 13
10	Literal
11	ExprTuple	14, 15
12	Literal
13	ExprTuple	16, 17
14	Operation	operator: 18 operands: 19
15	Operation	operator: 20 operand: 26
16	Literal
17	Operation	operator: 22 operands: 23
18	Literal
19	ExprTuple	24, 26
20	Literal
21	ExprTuple	26
22	Literal
23	ExprTuple	25, 26
24	Variable
25	Literal
26	Literal