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, Lambda, a, b, q
from proveit.logic import Equals, InSet
from proveit.numbers import Add, Integer, Mod, Mult

# build up the expression from sub-expressions
expr = Lambda(q, Conditional(Equals(a, Add(Mult(q, b), Mod(a, b))), InSet(q, Integer)))

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())

q \mapsto \left\{a = \left(\left(q \cdot b\right) + \left(a ~\textup{mod}~ b\right)\right) \textrm{ if } q \in \mathbb{Z}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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