Expression of type ExprTuple

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, ExprTuple, Lambda, N, a, b, x
from proveit.logic import Card, Equals, Forall, InSet, SetOfAll
from proveit.numbers import Integer, Interval, LessEq, Mod, NaturalPos

# build up the expression from sub-expressions
sub_expr1 = Interval(a, b)
sub_expr2 = Card(sub_expr1)
expr = ExprTuple(Lambda(N, Conditional(Forall(instance_param_or_params = [a, b], instance_expr = Equals(Card(SetOfAll(instance_param_or_params = [x], instance_element = Mod(x, N), domain = sub_expr1)), sub_expr2), domain = Integer, condition = LessEq(sub_expr2, N)), InSet(N, 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())

\left(N \mapsto \left\{\forall_{a, b \in \mathbb{Z}~|~|\{a~\ldotp \ldotp~b\}| \leq N}~\left(|\left\{x ~\textup{mod}~ N\right\}_{x \in \{a~\ldotp \ldotp~b\}}| = |\{a~\ldotp \ldotp~b\}|\right) \textrm{ if } N \in \mathbb{N}^+\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 43 body: 3
2	ExprTuple	43
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 41 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	43, 10
9	Lambda	parameters: 47 body: 11
10	Literal
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operands: 15
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18, 29
16	Literal
17	ExprTuple	19, 20, 21
18	Operation	operator: 32 operand: 27
19	Operation	operator: 41 operands: 23
20	Operation	operator: 41 operands: 24
21	Operation	operator: 25 operands: 26
22	ExprTuple	27
23	ExprTuple	48, 28
24	ExprTuple	49, 28
25	Literal
26	ExprTuple	29, 43
27	Operation	operator: 30 operand: 34
28	Literal
29	Operation	operator: 32 operand: 45
30	Literal
31	ExprTuple	34
32	Literal
33	ExprTuple	45
34	Lambda	parameter: 44 body: 36
35	ExprTuple	44
36	Conditional	value: 37 condition: 38
37	Operation	operator: 39 operands: 40
38	Operation	operator: 41 operands: 42
39	Literal
40	ExprTuple	44, 43
41	Literal
42	ExprTuple	44, 45
43	Variable
44	Variable
45	Operation	operator: 46 operands: 47
46	Literal
47	ExprTuple	48, 49
48	Variable
49	Variable