Expression of type Forall

from the theory of proveit.logic.booleans.disjunction

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_m, C_1_to_n
from proveit.logic import Boolean, Equals, Forall, Or, TRUE

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [A_1_to_m, C_1_to_n], instance_expr = Equals(Or(A_1_to_m, TRUE, C_1_to_n), TRUE), domain = Boolean)

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_{m}, C_{1}, C_{2}, \ldots, C_{n} \in \mathbb{B}}~\left(\left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m} \lor \top\lor C_{1} \lor  C_{2} \lor  \ldots \lor  C_{n}\right) = \top\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	19, 21
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12, 20
10	Literal
11	ExprTuple	13, 14
12	Operation	operator: 15 operands: 16
13	ExprRange	lambda_map: 17 start_index: 27 end_index: 25
14	ExprRange	lambda_map: 18 start_index: 27 end_index: 28
15	Literal
16	ExprTuple	19, 20, 21
17	Lambda	parameter: 38 body: 22
18	Lambda	parameter: 38 body: 23
19	ExprRange	lambda_map: 24 start_index: 27 end_index: 25
20	Literal
21	ExprRange	lambda_map: 26 start_index: 27 end_index: 28
22	Operation	operator: 30 operands: 29
23	Operation	operator: 30 operands: 31
24	Lambda	parameter: 38 body: 32
25	Variable
26	Lambda	parameter: 38 body: 33
27	Literal
28	Variable
29	ExprTuple	32, 34
30	Literal
31	ExprTuple	33, 34
32	IndexedVar	variable: 35 index: 38
33	IndexedVar	variable: 36 index: 38
34	Literal
35	Variable
36	Variable
37	ExprTuple	38
38	Variable