Expression of type Conditional ¶

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, 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 = Conditional(Forall(instance_param_or_params = [b, c, e], instance_expr = Equals(Mult(frac(Mult(a, b), c), frac(d, Mult(b, e))), Mult(frac(a, c), frac(d, e))), domain = ComplexNonZero), And(InSet(a, Complex), InSet(d, Complex)))

# 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\{\forall_{b, c, e \in \mathbb{C}^{\neq 0}}~\left(\left(\frac{a \cdot b}{c} \cdot \frac{d}{b \cdot e}\right) = \left(\frac{a}{c} \cdot \frac{d}{e}\right)\right) \textrm{ if } a \in \mathbb{C} ,  d \in \mathbb{C}\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

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

Expression of type Conditional¶

from the theory of proveit.numbers.division¶

Expression of type Conditional ¶

from the theory of proveit.numbers.division ¶