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, L, Lambda, x
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import IntervalCO, Mod, RealPos, zero

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(L, Conditional(Forall(instance_param_or_params = [x], instance_expr = Equals(Mod(x, L), x), domain = IntervalCO(zero, L)), InSet(L, 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(L \mapsto \left\{\forall_{x \in \left[0,L\right)}~\left(\left(x ~\textup{mod}~ L\right) = x\right) \textrm{ if } L \in \mathbb{R}^+\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: 27 body: 3
2	ExprTuple	27
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 17 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	27, 10
9	Lambda	parameter: 25 body: 12
10	Literal
11	ExprTuple	25
12	Conditional	value: 13 condition: 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19, 25
17	Literal
18	ExprTuple	25, 20
19	Operation	operator: 21 operands: 22
20	Operation	operator: 23 operands: 24
21	Literal
22	ExprTuple	25, 27
23	Literal
24	ExprTuple	26, 27
25	Variable
26	Literal
27	Variable