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 And, Equals, Exists, InSet
from proveit.numbers import Add, Integer, Mod, Mult, Real, RealPos

# build up the expression from sub-expressions
expr = Lambda([a, b], Conditional(Exists(instance_param_or_params = [q], instance_expr = Equals(a, Add(Mult(q, b), Mod(a, b))), domain = Integer), And(InSet(a, Real), InSet(b, RealPos))))

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())

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

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 32 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operand: 8
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8
6	Literal
7	ExprTuple	9, 10
8	Lambda	parameter: 33 body: 12
9	Operation	operator: 21 operands: 13
10	Operation	operator: 21 operands: 14
11	ExprTuple	33
12	Conditional	value: 15 condition: 16
13	ExprTuple	34, 17
14	ExprTuple	35, 18
15	Operation	operator: 19 operands: 20
16	Operation	operator: 21 operands: 22
17	Literal
18	Literal
19	Literal
20	ExprTuple	34, 23
21	Literal
22	ExprTuple	33, 24
23	Operation	operator: 25 operands: 26
24	Literal
25	Literal
26	ExprTuple	27, 28
27	Operation	operator: 29 operands: 30
28	Operation	operator: 31 operands: 32
29	Literal
30	ExprTuple	33, 35
31	Literal
32	ExprTuple	34, 35
33	Variable
34	Variable
35	Variable