Expression of type Lambda

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 Conditional, ExprRange, Function, IndexedVar, Lambda, Q, Variable, alpha, beta, c, delta, f, gamma, j
from proveit.numbers import one
from proveit.physics.quantum import Qmult, bra_varphi, ket_psi

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = [ExprRange(sub_expr1, IndexedVar(c, sub_expr1), one, j)]
expr = Lambda(sub_expr2, Conditional(Qmult(bra_varphi, alpha, Function(f, sub_expr2), beta, ket_psi, gamma, bra_varphi, delta), Function(Q, sub_expr2)))

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(c_{1}, c_{2}, \ldots, c_{j}\right) \mapsto \left\{\langle \varphi \rvert \thinspace \alpha \thinspace f\left(c_{1}, c_{2}, \ldots, c_{j}\right) \thinspace \beta \thinspace \lvert \psi \rangle \thinspace \gamma \thinspace \langle \varphi \rvert \thinspace \delta \textrm{ if } Q\left(c_{1}, c_{2}, \ldots, c_{j}\right)\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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