Expression of type Lambda

from the theory of proveit.numbers.number_sets.real_numbers

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, a, b, c, x
from proveit.logic import InSet
from proveit.numbers import IntervalOC, Mult

# build up the expression from sub-expressions
expr = Lambda(x, Conditional(InSet(Mult(c, x), IntervalOC(Mult(c, a), Mult(c, b))), InSet(x, IntervalOC(a, b))))

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())

x \mapsto \left\{\left(c \cdot x\right) \in \left(c \cdot a,c \cdot b\right] \textrm{ if } x \in \left(a,b\right]\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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