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.core_expr_types import a_1_to_i, b_1_to_j, c_1_to_k, d_1_to_j
from proveit.logic import Equals, Forall

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a_1_to_i, b_1_to_j, c_1_to_k, d_1_to_j], instance_expr = Equals([a_1_to_i, b_1_to_j, c_1_to_k], [a_1_to_i, d_1_to_j, c_1_to_k]).with_wrapping_at(2), condition = Equals([b_1_to_j], [d_1_to_j]))

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_{a_{1}, a_{2}, \ldots, a_{i}, b_{1}, b_{2}, \ldots, b_{j}, c_{1}, c_{2}, \ldots, c_{k}, d_{1}, d_{2}, \ldots, d_{j}~|~\left(b_{1}, b_{2}, \ldots, b_{j}\right) = \left(d_{1}, d_{2}, \ldots, d_{j}\right)}~\left(\begin{array}{c} \begin{array}{l} \left(a_{1}, a_{2}, \ldots, a_{i},b_{1}, b_{2}, \ldots, b_{j},c_{1}, c_{2}, \ldots, c_{k}\right) =  \\ \left(a_{1}, a_{2}, \ldots, a_{i},d_{1}, d_{2}, \ldots, d_{j},c_{1}, c_{2}, \ldots, c_{k}\right) \end{array} \end{array}\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: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 4 body: 5
4	ExprTuple	15, 17, 16, 18
5	Conditional	value: 6 condition: 7
6	Operation	operator: 9 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	13, 14
11	ExprTuple	15, 17, 16
12	ExprTuple	15, 18, 16
13	ExprTuple	17
14	ExprTuple	18
15	ExprRange	lambda_map: 19 start_index: 25 end_index: 20
16	ExprRange	lambda_map: 21 start_index: 25 end_index: 22
17	ExprRange	lambda_map: 23 start_index: 25 end_index: 26
18	ExprRange	lambda_map: 24 start_index: 25 end_index: 26
19	Lambda	parameter: 36 body: 27
20	Variable
21	Lambda	parameter: 36 body: 28
22	Variable
23	Lambda	parameter: 36 body: 29
24	Lambda	parameter: 36 body: 30
25	Literal
26	Variable
27	IndexedVar	variable: 31 index: 36
28	IndexedVar	variable: 32 index: 36
29	IndexedVar	variable: 33 index: 36
30	IndexedVar	variable: 34 index: 36
31	Variable
32	Variable
33	Variable
34	Variable
35	ExprTuple	36
36	Variable