Expression of type Lambda

from the theory of proveit.numbers.division

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, d, e
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Complex, ComplexNonZero, Mult, frac

# build up the expression from sub-expressions
expr = Lambda([a, d], Conditional(Forall(instance_param_or_params = [b, c, e], instance_expr = Equals(Mult(frac(a, Mult(b, c)), frac(Mult(c, d), e)), Mult(frac(a, b), frac(d, e))), domain = ComplexNonZero), And(InSet(a, Complex), InSet(d, Complex))))

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, d\right) \mapsto \left\{\forall_{b, c, e \in \mathbb{C}^{\neq 0}}~\left(\left(\frac{a}{b \cdot c} \cdot \frac{c \cdot d}{e}\right) = \left(\frac{a}{b} \cdot \frac{d}{e}\right)\right) \textrm{ if } a \in \mathbb{C} ,  d \in \mathbb{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	45, 52
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 20 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameters: 11 body: 12
9	Operation	operator: 31 operands: 13
10	Operation	operator: 31 operands: 14
11	ExprTuple	50, 51, 46
12	Conditional	value: 15 condition: 16
13	ExprTuple	45, 17
14	ExprTuple	52, 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Literal
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	24, 25, 26
22	Operation	operator: 48 operands: 27
23	Operation	operator: 48 operands: 28
24	Operation	operator: 31 operands: 29
25	Operation	operator: 31 operands: 30
26	Operation	operator: 31 operands: 32
27	ExprTuple	33, 34
28	ExprTuple	35, 36
29	ExprTuple	50, 37
30	ExprTuple	51, 37
31	Literal
32	ExprTuple	46, 37
33	Operation	operator: 41 operands: 38
34	Operation	operator: 41 operands: 39
35	Operation	operator: 41 operands: 40
36	Operation	operator: 41 operands: 42
37	Literal
38	ExprTuple	45, 43
39	ExprTuple	44, 46
40	ExprTuple	45, 50
41	Literal
42	ExprTuple	52, 46
43	Operation	operator: 48 operands: 47
44	Operation	operator: 48 operands: 49
45	Variable
46	Variable
47	ExprTuple	50, 51
48	Literal
49	ExprTuple	51, 52
50	Variable
51	Variable
52	Variable