Theorem condition_merger_reduction of type Forall

from the theory of proveit.core_expr_types.conditionals

see dependencies

import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.core_expr_types.conditionals import condition_merger_reduction

# check that the built expression is the same as the stored expression
assert condition_merger_reduction.expr == stored_expr
assert condition_merger_reduction.expr._style_id == stored_expr._style_id
print("Passed sanity check: condition_merger_reduction matches stored_expr")

Passed sanity check: condition_merger_reduction matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{m, n \in \mathbb{N}}~\left[\forall_{a, Q_{1}, Q_{2}, \ldots, Q_{m}, R_{1}, R_{2}, \ldots, R_{n}}~\left(\begin{array}{c} \begin{array}{l} \left\{a \textrm{ if } Q_{1} \land  Q_{2} \land  \ldots \land  Q_{m} ,  R_{1} \land  R_{2} \land  \ldots \land  R_{n}\right.. \\  = \left\{a \textrm{ if } Q_{1} ,  Q_{2} ,  \ldots ,  Q_{m}, R_{1} ,  R_{2} ,  \ldots ,  R_{n}\right.. \end{array} \end{array}\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: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 3 body: 4
3	ExprTuple	36, 39
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 31 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	11, 12
10	Lambda	parameters: 13 body: 14
11	Operation	operator: 16 operands: 15
12	Operation	operator: 16 operands: 17
13	ExprTuple	24, 33, 34
14	Operation	operator: 18 operands: 19
15	ExprTuple	36, 20
16	Literal
17	ExprTuple	39, 20
18	Literal
19	ExprTuple	21, 22
20	Literal
21	Conditional	value: 24 condition: 23
22	Conditional	value: 24 condition: 25
23	Operation	operator: 31 operands: 26
24	Variable
25	Operation	operator: 31 operands: 27
26	ExprTuple	28, 29
27	ExprTuple	33, 34
28	Operation	operator: 31 operands: 30
29	Operation	operator: 31 operands: 32
30	ExprTuple	33
31	Literal
32	ExprTuple	34
33	ExprRange	lambda_map: 35 start_index: 38 end_index: 36
34	ExprRange	lambda_map: 37 start_index: 38 end_index: 39
35	Lambda	parameter: 45 body: 40
36	Variable
37	Lambda	parameter: 45 body: 41
38	Literal
39	Variable
40	IndexedVar	variable: 42 index: 45
41	IndexedVar	variable: 43 index: 45
42	Variable
43	Variable
44	ExprTuple	45
45	Variable