Expression of type Conditional ¶

from the theory of proveit.logic.equality ¶

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, ExprRange, IndexedVar, Variable, n, x
from proveit.core_expr_types import x_1_to_np1
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Add, NaturalPos, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(Forall(instance_param_or_params = [x_1_to_np1], instance_expr = Equals(IndexedVar(x, one), IndexedVar(x, Add(n, one))), condition = ExprRange(sub_expr1, Equals(IndexedVar(x, sub_expr1), IndexedVar(x, Add(sub_expr1, one))), one, n)), InSet(n, NaturalPos))

# 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_{x_{1}, x_{2}, \ldots, x_{n + 1}~|~\left(x_{1} = x_{1 + 1}\right), \left(x_{2} = x_{2 + 1}\right), \ldots, \left(x_{n} = x_{n + 1}\right)}~\left(x_{1} = x_{n + 1}\right) \textrm{ if } n \in \mathbb{N}^+\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: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	29, 8
7	Lambda	parameters: 9 body: 10
8	Literal
9	ExprTuple	11
10	Conditional	value: 12 condition: 13
11	ExprRange	lambda_map: 14 start_index: 39 end_index: 24
12	Operation	operator: 27 operands: 15
13	Operation	operator: 16 operands: 17
14	Lambda	parameter: 38 body: 30
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	20
18	IndexedVar	variable: 33 index: 39
19	IndexedVar	variable: 33 index: 24
20	ExprRange	lambda_map: 23 start_index: 39 end_index: 29
21	ExprTuple	39
22	ExprTuple	24
23	Lambda	parameter: 38 body: 25
24	Operation	operator: 36 operands: 26
25	Operation	operator: 27 operands: 28
26	ExprTuple	29, 39
27	Literal
28	ExprTuple	30, 31
29	Variable
30	IndexedVar	variable: 33 index: 38
31	IndexedVar	variable: 33 index: 35
32	ExprTuple	38
33	Variable
34	ExprTuple	35
35	Operation	operator: 36 operands: 37
36	Literal
37	ExprTuple	38, 39
38	Variable
39	Literal

Expression of type Conditional¶

from the theory of proveit.logic.equality¶

Expression of type Conditional ¶

from the theory of proveit.logic.equality ¶