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, c, x
from proveit.logic import Bijections, Forall, InSet
from proveit.numbers import Integer, Interval, Mod, NaturalPos, one, subtract, zero

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(N, Conditional(Forall(instance_param_or_params = [a, b, c], instance_expr = InSet(Lambda(x, Mod(x, N)), Bijections(Interval(a, b), Interval(zero, subtract(N, one)))), domain = Integer), 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, c \in \mathbb{Z}}~\left(\left[x \mapsto \left(x ~\textup{mod}~ N\right)\right] \in \left[\{a~\ldotp \ldotp~b\} \xrightarrow[\text{onto}]{\text{1-to-1}} \{0~\ldotp \ldotp~N - 1\}\right]\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: 47 body: 3
2	ExprTuple	47
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 29 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	47, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	41, 42, 35
12	Conditional	value: 13 condition: 14
13	Operation	operator: 29 operands: 15
14	Operation	operator: 16 operands: 17
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	20, 21, 22
18	Lambda	parameter: 37 body: 24
19	Operation	operator: 25 operands: 26
20	Operation	operator: 29 operands: 27
21	Operation	operator: 29 operands: 28
22	Operation	operator: 29 operands: 30
23	ExprTuple	37
24	Operation	operator: 31 operands: 32
25	Literal
26	ExprTuple	33, 34
27	ExprTuple	41, 36
28	ExprTuple	42, 36
29	Literal
30	ExprTuple	35, 36
31	Literal
32	ExprTuple	37, 47
33	Operation	operator: 39 operands: 38
34	Operation	operator: 39 operands: 40
35	Variable
36	Literal
37	Variable
38	ExprTuple	41, 42
39	Literal
40	ExprTuple	43, 44
41	Variable
42	Variable
43	Literal
44	Operation	operator: 45 operands: 46
45	Literal
46	ExprTuple	47, 48
47	Variable
48	Operation	operator: 49 operand: 51
49	Literal
50	ExprTuple	51
51	Literal