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, Forall, InSet
from proveit.numbers import Interval, Mod, NaturalPos, one, subtract, zero

# build up the expression from sub-expressions
expr = Lambda(L, Conditional(Forall(instance_param_or_params = [x], instance_expr = Equals(Mod(x, L), x), domain = Interval(zero, subtract(L, one))), InSet(L, NaturalPos)))

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())

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

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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