Expression of type Forall

from the theory of proveit.core_expr_types.tuples

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 ExprRange, IndexedVar, Variable, a, b, m
from proveit.logic import Equals, Forall
from proveit.numbers import Add, NaturalPos, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(a, sub_expr1)
sub_expr3 = Add(m, one)
sub_expr4 = IndexedVar(b, sub_expr1)
sub_expr5 = ExprRange(sub_expr1, sub_expr2, one, sub_expr3)
sub_expr6 = ExprRange(sub_expr1, sub_expr4, one, sub_expr3)
sub_expr7 = Equals(sub_expr2, sub_expr4)
sub_expr8 = ExprRange(sub_expr1, sub_expr2, one, m)
sub_expr9 = ExprRange(sub_expr1, sub_expr4, one, m)
expr = Forall(instance_param_or_params = [m], instance_expr = Forall(instance_param_or_params = [sub_expr5, sub_expr6], instance_expr = Equals([sub_expr5], [sub_expr6]), condition = ExprRange(sub_expr1, sub_expr7, one, sub_expr3)), domain = NaturalPos, condition = Forall(instance_param_or_params = [sub_expr8, sub_expr9], instance_expr = Equals([sub_expr8], [sub_expr9]), condition = ExprRange(sub_expr1, sub_expr7, one, m)))

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())

\forall_{m \in \mathbb{N}^+~|~\forall_{a_{1}, a_{2}, \ldots, a_{m}, b_{1}, b_{2}, \ldots, b_{m}~|~\left(a_{1} = b_{1}\right), \left(a_{2} = b_{2}\right), \ldots, \left(a_{m} = b_{m}\right)}~\left(\left(a_{1}, a_{2}, \ldots, a_{m}\right) = \left(b_{1}, b_{2}, \ldots, b_{m}\right)\right)}~\left[\forall_{a_{1}, a_{2}, \ldots, a_{m + 1}, b_{1}, b_{2}, \ldots, b_{m + 1}~|~\left(a_{1} = b_{1}\right), \left(a_{2} = b_{2}\right), \ldots, \left(a_{m + 1} = b_{m + 1}\right)}~\left(\left(a_{1}, a_{2}, \ldots, a_{m + 1}\right) = \left(b_{1}, b_{2}, \ldots, b_{m + 1}\right)\right)\right]

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 16 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 48 body: 4
3	ExprTuple	48
4	Conditional	value: 5 condition: 6
5	Operation	operator: 16 operand: 9
6	Operation	operator: 34 operands: 8
7	ExprTuple	9
8	ExprTuple	10, 11
9	Lambda	parameters: 12 body: 13
10	Operation	operator: 14 operands: 15
11	Operation	operator: 16 operand: 21
12	ExprTuple	31, 32
13	Conditional	value: 18 condition: 19
14	Literal
15	ExprTuple	48, 20
16	Literal
17	ExprTuple	21
18	Operation	operator: 50 operands: 22
19	Operation	operator: 34 operands: 23
20	Literal
21	Lambda	parameters: 24 body: 25
22	ExprTuple	26, 27
23	ExprTuple	28
24	ExprTuple	42, 43
25	Conditional	value: 29 condition: 30
26	ExprTuple	31
27	ExprTuple	32
28	ExprRange	lambda_map: 44 start_index: 47 end_index: 36
29	Operation	operator: 50 operands: 33
30	Operation	operator: 34 operands: 35
31	ExprRange	lambda_map: 45 start_index: 47 end_index: 36
32	ExprRange	lambda_map: 46 start_index: 47 end_index: 36
33	ExprTuple	37, 38
34	Literal
35	ExprTuple	39
36	Operation	operator: 40 operands: 41
37	ExprTuple	42
38	ExprTuple	43
39	ExprRange	lambda_map: 44 start_index: 47 end_index: 48
40	Literal
41	ExprTuple	48, 47
42	ExprRange	lambda_map: 45 start_index: 47 end_index: 48
43	ExprRange	lambda_map: 46 start_index: 47 end_index: 48
44	Lambda	parameter: 57 body: 49
45	Lambda	parameter: 57 body: 52
46	Lambda	parameter: 57 body: 53
47	Literal
48	Variable
49	Operation	operator: 50 operands: 51
50	Literal
51	ExprTuple	52, 53
52	IndexedVar	variable: 54 index: 57
53	IndexedVar	variable: 55 index: 57
54	Variable
55	Variable
56	ExprTuple	57
57	Variable