Expression of type Lambda

from the theory of proveit.numbers.addition.subtraction

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, Complex, Neg, subtract

# build up the expression from sub-expressions
expr = Lambda([a, b, c], Conditional(Equals(subtract(b, c), Neg(a)), And(InSet(a, Complex), InSet(b, Complex), InSet(c, Complex), 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(b - c\right) = \left(-a\right) \textrm{ if } a \in \mathbb{C} ,  b \in \mathbb{C} ,  c \in \mathbb{C} ,  \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	30, 31, 29
2	Conditional	value: 3 condition: 4
3	Operation	operator: 20 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11, 12, 13
8	Operation	operator: 27 operands: 14
9	Operation	operator: 25 operand: 30
10	Operation	operator: 18 operands: 16
11	Operation	operator: 18 operands: 17
12	Operation	operator: 18 operands: 19
13	Operation	operator: 20 operands: 21
14	ExprTuple	31, 22
15	ExprTuple	30
16	ExprTuple	30, 23
17	ExprTuple	31, 23
18	Literal
19	ExprTuple	29, 23
20	Literal
21	ExprTuple	24, 29
22	Operation	operator: 25 operand: 29
23	Literal
24	Operation	operator: 27 operands: 28
25	Literal
26	ExprTuple	29
27	Literal
28	ExprTuple	30, 31
29	Variable
30	Variable
31	Variable