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, a, b, j
from proveit.logic import InSet
from proveit.numbers import Add, Interval, subtract, three

# build up the expression from sub-expressions
expr = Lambda(j, Conditional(subtract(j, three), InSet(j, Interval(Add(a, three), Add(b, three)))))

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())

j \mapsto \left\{j - 3 \textrm{ if } j \in \{a + 3~\ldotp \ldotp~b + 3\}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 9 body: 2
1	ExprTuple	9
2	Conditional	value: 3 condition: 4
3	Operation	operator: 18 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	9, 8
6	Literal
7	ExprTuple	9, 10
8	Operation	operator: 11 operand: 22
9	Variable
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	22
13	Literal
14	ExprTuple	15, 16
15	Operation	operator: 18 operands: 17
16	Operation	operator: 18 operands: 19
17	ExprTuple	20, 22
18	Literal
19	ExprTuple	21, 22
20	Variable
21	Variable
22	Literal