Expression of type Lambda

from the theory of proveit.physics.quantum.circuits

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 IndexedVar, Lambda, N, Variable, n
from proveit.logic import Equals
from proveit.numbers import Add, one, subtract

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda(sub_expr1, Equals(IndexedVar(N, sub_expr1), Add(IndexedVar(N, subtract(sub_expr1, one)), IndexedVar(n, sub_expr1))))

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())

{_{-}a} \mapsto \left(N_{{_{-}a}} = \left(N_{{_{-}a} - 1} + n_{{_{-}a}}\right)\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 16 body: 1
1	Operation	operator: 2 operands: 3
2	Literal
3	ExprTuple	4, 5
4	IndexedVar	variable: 9 index: 16
5	Operation	operator: 14 operands: 6
6	ExprTuple	7, 8
7	IndexedVar	variable: 9 index: 13
8	IndexedVar	variable: 11 index: 16
9	Variable
10	ExprTuple	13
11	Variable
12	ExprTuple	16
13	Operation	operator: 14 operands: 15
14	Literal
15	ExprTuple	16, 17
16	Variable
17	Operation	operator: 18 operand: 20
18	Literal
19	ExprTuple	20
20	Literal