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 import A, B, ExprRange, IndexedVar, Variable, m
from proveit.core_expr_types import A_1_to_m, B_1_to_m
from proveit.logic import Boolean, Forall, Implies, Or
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Forall(instance_param_or_params = [A_1_to_m, B_1_to_m], instance_expr = Or(B_1_to_m), domain = Boolean, conditions = [Or(A_1_to_m), ExprRange(sub_expr1, Implies(IndexedVar(A, sub_expr1), IndexedVar(B, sub_expr1)), 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_{A_{1}, A_{2}, \ldots, A_{m}, B_{1}, B_{2}, \ldots, B_{m} \in \mathbb{B}~|~A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m},\left(A_{1} \Rightarrow B_{1}\right), \left(A_{2} \Rightarrow B_{2}\right), \ldots, \left(A_{m} \Rightarrow B_{m}\right)}~\left(B_{1} \lor  B_{2} \lor  \ldots \lor  B_{m}\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	24, 11
5	Conditional	value: 6 condition: 7
6	Operation	operator: 19 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11
9	Literal
10	ExprTuple	12, 13, 14, 15
11	ExprRange	lambda_map: 16 start_index: 30 end_index: 31
12	ExprRange	lambda_map: 17 start_index: 30 end_index: 31
13	ExprRange	lambda_map: 18 start_index: 30 end_index: 31
14	Operation	operator: 19 operands: 20
15	ExprRange	lambda_map: 21 start_index: 30 end_index: 31
16	Lambda	parameter: 40 body: 36
17	Lambda	parameter: 40 body: 22
18	Lambda	parameter: 40 body: 23
19	Literal
20	ExprTuple	24
21	Lambda	parameter: 40 body: 25
22	Operation	operator: 27 operands: 26
23	Operation	operator: 27 operands: 28
24	ExprRange	lambda_map: 29 start_index: 30 end_index: 31
25	Operation	operator: 32 operands: 33
26	ExprTuple	35, 34
27	Literal
28	ExprTuple	36, 34
29	Lambda	parameter: 40 body: 35
30	Literal
31	Variable
32	Literal
33	ExprTuple	35, 36
34	Literal
35	IndexedVar	variable: 37 index: 40
36	IndexedVar	variable: 38 index: 40
37	Variable
38	Variable
39	ExprTuple	40
40	Variable