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, x, y
from proveit.logic import And, Equals, Implies, InSet
from proveit.numbers import Add, Integer, IntervalOO, LessEq, RealPos, one, subtract

# build up the expression from sub-expressions
expr = Lambda([a, b, x, y], Conditional(Implies(InSet(y, IntervalOO(subtract(x, a), Add(x, b))), Equals(y, x)), And(InSet(a, RealPos), InSet(b, RealPos), InSet(x, Integer), InSet(y, Integer), LessEq(a, one), LessEq(b, one))))

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, x, y\right) \mapsto \left\{\left(y \in \left(x - a,x + b\right)\right) \Rightarrow \left(y = x\right) \textrm{ if } a \in \mathbb{R}^+ ,  b \in \mathbb{R}^+ ,  x \in \mathbb{Z} ,  y \in \mathbb{Z} ,  a \leq 1 ,  b \leq 1\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	45, 42, 41, 30
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12, 13, 14, 15, 16
9	Operation	operator: 23 operands: 17
10	Operation	operator: 18 operands: 19
11	Operation	operator: 23 operands: 20
12	Operation	operator: 23 operands: 21
13	Operation	operator: 23 operands: 22
14	Operation	operator: 23 operands: 24
15	Operation	operator: 26 operands: 25
16	Operation	operator: 26 operands: 27
17	ExprTuple	30, 28
18	Literal
19	ExprTuple	30, 41
20	ExprTuple	45, 29
21	ExprTuple	42, 29
22	ExprTuple	41, 31
23	Literal
24	ExprTuple	30, 31
25	ExprTuple	45, 32
26	Literal
27	ExprTuple	42, 32
28	Operation	operator: 33 operands: 34
29	Literal
30	Variable
31	Literal
32	Literal
33	Literal
34	ExprTuple	35, 36
35	Operation	operator: 38 operands: 37
36	Operation	operator: 38 operands: 39
37	ExprTuple	41, 40
38	Literal
39	ExprTuple	41, 42
40	Operation	operator: 43 operand: 45
41	Variable
42	Variable
43	Literal
44	ExprTuple	45
45	Variable