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 And, Forall, InSet
from proveit.numbers import IntervalCO, Mult, Real

# build up the expression from sub-expressions
expr = Lambda([a, b, c], Conditional(Forall(instance_param_or_params = [x], instance_expr = InSet(Mult(c, x), IntervalCO(Mult(c, a), Mult(c, b))), domain = IntervalCO(a, b)), And(InSet(a, Real), InSet(b, Real), InSet(c, Real))))

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, c\right) \mapsto \left\{\forall_{x \in \left[a,b\right)}~\left(\left(c \cdot x\right) \in \left[c \cdot a,c \cdot b\right)\right) \textrm{ if } a \in \mathbb{R} ,  b \in \mathbb{R} ,  c \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	37, 39, 38
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	10, 11, 12
9	Lambda	parameter: 31 body: 14
10	Operation	operator: 22 operands: 15
11	Operation	operator: 22 operands: 16
12	Operation	operator: 22 operands: 17
13	ExprTuple	31
14	Conditional	value: 18 condition: 19
15	ExprTuple	37, 20
16	ExprTuple	39, 20
17	ExprTuple	38, 20
18	Operation	operator: 22 operands: 21
19	Operation	operator: 22 operands: 23
20	Literal
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	31, 26
24	Operation	operator: 35 operands: 27
25	Operation	operator: 29 operands: 28
26	Operation	operator: 29 operands: 30
27	ExprTuple	38, 31
28	ExprTuple	32, 33
29	Literal
30	ExprTuple	37, 39
31	Variable
32	Operation	operator: 35 operands: 34
33	Operation	operator: 35 operands: 36
34	ExprTuple	38, 37
35	Literal
36	ExprTuple	38, 39
37	Variable
38	Variable
39	Variable