Expression of type Forall

from the theory of proveit.logic.equality

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, c, f, fa, fx, x
from proveit.logic import Equals, Forall, Implies

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [f, x, a, c], instance_expr = Implies(Equals(x, a), Implies(Equals(fa, c), Equals(fx, c))))

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_{f, x, a, c}~\left(\left(x = a\right) \Rightarrow \left(\left(f\left(a\right) = c\right) \Rightarrow \left(f\left(x\right) = c\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: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 4 body: 5
4	ExprTuple	21, 24, 23, 19
5	Operation	operator: 10 operands: 6
6	ExprTuple	7, 8
7	Operation	operator: 15 operands: 9
8	Operation	operator: 10 operands: 11
9	ExprTuple	24, 23
10	Literal
11	ExprTuple	12, 13
12	Operation	operator: 15 operands: 14
13	Operation	operator: 15 operands: 16
14	ExprTuple	17, 19
15	Literal
16	ExprTuple	18, 19
17	Operation	operator: 21 operand: 23
18	Operation	operator: 21 operand: 24
19	Variable
20	ExprTuple	23
21	Variable
22	ExprTuple	24
23	Variable
24	Variable