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, N, a, b
from proveit.logic import And, InSet
from proveit.numbers import ModAbs, Real, RealPos, greater_eq, subtract

# build up the expression from sub-expressions
expr = Lambda([a, b, N], Conditional(greater_eq(ModAbs(subtract(a, b), N), subtract(ModAbs(a, N), ModAbs(b, N))), And(InSet(a, Real), InSet(b, Real), InSet(N, 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, N\right) \mapsto \left\{\left|a - b\right|_{\textup{mod}\thinspace N} \geq \left(\left|a\right|_{\textup{mod}\thinspace N} - \left|b\right|_{\textup{mod}\thinspace N}\right) \textrm{ if } a \in \mathbb{R} ,  b \in \mathbb{R} ,  N \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: 1 body: 2
1	ExprTuple	30, 37, 36
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12, 13
9	Operation	operator: 27 operands: 14
10	Operation	operator: 32 operands: 15
11	Operation	operator: 18 operands: 16
12	Operation	operator: 18 operands: 17
13	Operation	operator: 18 operands: 19
14	ExprTuple	20, 21
15	ExprTuple	22, 36
16	ExprTuple	30, 23
17	ExprTuple	37, 23
18	Literal
19	ExprTuple	36, 24
20	Operation	operator: 32 operands: 25
21	Operation	operator: 34 operand: 29
22	Operation	operator: 27 operands: 28
23	Literal
24	Literal
25	ExprTuple	30, 36
26	ExprTuple	29
27	Literal
28	ExprTuple	30, 31
29	Operation	operator: 32 operands: 33
30	Variable
31	Operation	operator: 34 operand: 37
32	Literal
33	ExprTuple	37, 36
34	Literal
35	ExprTuple	37
36	Variable
37	Variable