Expression of type Implies

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 A, B, C, alpha, beta, delta, gamma
from proveit.linear_algebra import VecAdd
from proveit.logic import Equals, Implies, InClass
from proveit.physics.quantum import Qmult, QmultCodomain, bra_varphi, ket_psi

# build up the expression from sub-expressions
sub_expr1 = Qmult(bra_varphi, alpha, VecAdd(A, B, C), beta, ket_psi, gamma, bra_varphi, delta)
expr = Implies(InClass(sub_expr1, QmultCodomain), Equals(sub_expr1, VecAdd(Qmult(bra_varphi, alpha, A, beta, ket_psi, gamma, bra_varphi, delta), Qmult(bra_varphi, alpha, B, beta, ket_psi, gamma, bra_varphi, delta), Qmult(bra_varphi, alpha, C, beta, ket_psi, gamma, bra_varphi, delta))).with_wrapping_at(2)).with_wrapping_at(2)

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())

\begin{array}{c} \begin{array}{l} \left(\left(\langle \varphi \rvert \thinspace \alpha \thinspace \left(A + B + C\right) \thinspace \beta \thinspace \lvert \psi \rangle \thinspace \gamma \thinspace \langle \varphi \rvert \thinspace \delta\right) \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}\right) \Rightarrow  \\ \left(\begin{array}{c} \begin{array}{l} \left(\langle \varphi \rvert \thinspace \alpha \thinspace \left(A + B + C\right) \thinspace \beta \thinspace \lvert \psi \rangle \thinspace \gamma \thinspace \langle \varphi \rvert \thinspace \delta\right) =  \\ \left(\left(\langle \varphi \rvert \thinspace \alpha \thinspace A \thinspace \beta \thinspace \lvert \psi \rangle \thinspace \gamma \thinspace \langle \varphi \rvert \thinspace \delta\right) + \left(\langle \varphi \rvert \thinspace \alpha \thinspace B \thinspace \beta \thinspace \lvert \psi \rangle \thinspace \gamma \thinspace \langle \varphi \rvert \thinspace \delta\right) + \left(\langle \varphi \rvert \thinspace \alpha \thinspace C \thinspace \beta \thinspace \lvert \psi \rangle \thinspace \gamma \thinspace \langle \varphi \rvert \thinspace \delta\right)\right) \end{array} \end{array}\right) \end{array} \end{array}

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.	()	(2)	('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: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	10, 9
7	Literal
8	ExprTuple	10, 11
9	Literal
10	Operation	operator: 22 operands: 12
11	Operation	operator: 18 operands: 13
12	ExprTuple	31, 26, 14, 28, 29, 30, 31, 32
13	ExprTuple	15, 16, 17
14	Operation	operator: 18 operands: 19
15	Operation	operator: 22 operands: 20
16	Operation	operator: 22 operands: 21
17	Operation	operator: 22 operands: 23
18	Literal
19	ExprTuple	24, 25, 27
20	ExprTuple	31, 26, 24, 28, 29, 30, 31, 32
21	ExprTuple	31, 26, 25, 28, 29, 30, 31, 32
22	Literal
23	ExprTuple	31, 26, 27, 28, 29, 30, 31, 32
24	Variable
25	Variable
26	Variable
27	Variable
28	Variable
29	Operation	operator: 33 operand: 37
30	Variable
31	Operation	operator: 35 operand: 38
32	Variable
33	Literal
34	ExprTuple	37
35	Literal
36	ExprTuple	38
37	Variable
38	Variable