Expression of type Lambda

from the theory of proveit.numbers.summation

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, Lambda, S, k
from proveit.logic import InSet
from proveit.numbers import Less
from proveit.numbers.summation import ak, bk

# build up the expression from sub-expressions
expr = Lambda(k, Conditional(Less(ak, bk), InSet(k, S)))

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())

k \mapsto \left\{a\left(k\right) < b\left(k\right) \textrm{ if } k \in S\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 14 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	14, 10
8	Operation	operator: 11 operand: 14
9	Operation	operator: 12 operand: 14
10	Variable
11	Variable
12	Variable
13	ExprTuple	14
14	Variable