Expression of type Lambda

from the theory of proveit.numbers.modular

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, L, Lambda, x
from proveit.logic import Equals, InSet
from proveit.numbers import Interval, Mod, one, subtract, zero

# build up the expression from sub-expressions
expr = Lambda(x, Conditional(Equals(Mod(x, L), x), InSet(x, Interval(zero, subtract(L, one)))))

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())

x \mapsto \left\{\left(x ~\textup{mod}~ L\right) = x \textrm{ if } x \in \{0~\ldotp \ldotp~L - 1\}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 15 body: 2
1	ExprTuple	15
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 15
7	Literal
8	ExprTuple	15, 10
9	Operation	operator: 11 operands: 12
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	15, 20
13	Literal
14	ExprTuple	16, 17
15	Variable
16	Literal
17	Operation	operator: 18 operands: 19
18	Literal
19	ExprTuple	20, 21
20	Variable
21	Operation	operator: 22 operand: 24
22	Literal
23	ExprTuple	24
24	Literal