Expression of type Lambda

from the theory of proveit.numbers.negation

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
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Natural, subtract

# build up the expression from sub-expressions
expr = Lambda([a, b, c], Conditional(Equals(subtract(c, a), b), And(InSet(a, Natural), InSet(b, Natural), InSet(c, Natural), Equals(Add(a, b), c))))

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\{\left(c - a\right) = b \textrm{ if } a \in \mathbb{N} ,  b \in \mathbb{N} ,  c \in \mathbb{N} ,  \left(a + b\right) = c\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	28, 29, 23
2	Conditional	value: 3 condition: 4
3	Operation	operator: 18 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 29
6	Literal
7	ExprTuple	9, 10, 11, 12
8	Operation	operator: 26 operands: 13
9	Operation	operator: 16 operands: 14
10	Operation	operator: 16 operands: 15
11	Operation	operator: 16 operands: 17
12	Operation	operator: 18 operands: 19
13	ExprTuple	23, 20
14	ExprTuple	28, 21
15	ExprTuple	29, 21
16	Literal
17	ExprTuple	23, 21
18	Literal
19	ExprTuple	22, 23
20	Operation	operator: 24 operand: 28
21	Literal
22	Operation	operator: 26 operands: 27
23	Variable
24	Literal
25	ExprTuple	28
26	Literal
27	ExprTuple	28, 29
28	Variable
29	Variable