Expression of type ExprTuple

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, ExprTuple, 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 = ExprTuple(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(\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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	46, 53
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 21 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11
9	Lambda	parameters: 12 body: 13
10	Operation	operator: 32 operands: 14
11	Operation	operator: 32 operands: 15
12	ExprTuple	51, 52, 47
13	Conditional	value: 16 condition: 17
14	ExprTuple	46, 18
15	ExprTuple	53, 18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operands: 22
18	Literal
19	Literal
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	25, 26, 27
23	Operation	operator: 49 operands: 28
24	Operation	operator: 49 operands: 29
25	Operation	operator: 32 operands: 30
26	Operation	operator: 32 operands: 31
27	Operation	operator: 32 operands: 33
28	ExprTuple	34, 35
29	ExprTuple	36, 37
30	ExprTuple	51, 38
31	ExprTuple	52, 38
32	Literal
33	ExprTuple	47, 38
34	Operation	operator: 42 operands: 39
35	Operation	operator: 42 operands: 40
36	Operation	operator: 42 operands: 41
37	Operation	operator: 42 operands: 43
38	Literal
39	ExprTuple	46, 44
40	ExprTuple	45, 47
41	ExprTuple	46, 51
42	Literal
43	ExprTuple	53, 47
44	Operation	operator: 49 operands: 48
45	Operation	operator: 49 operands: 50
46	Variable
47	Variable
48	ExprTuple	51, 52
49	Literal
50	ExprTuple	52, 53
51	Variable
52	Variable
53	Variable