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Theorem Sep-forall
∀ a, h. a ∈ s ∧ aP0(a)(h) → aP(a)(h) ⊦ ((aP0 ⊗_ s))(h) → ((aP ⊗_ s))(h)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Sep-eq
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 8
Proof steps: 19
Used lemmas:
Sep-ins
,
Sep-emp
,
Used spec theorems:
set-basic
/
Extension
set-basic
/
indef
heap-sep
/
sep
heap-sep
/
split-union
Used simplifier rules:
heap-sep
/
emp
set-basic
/
size-zero
set-basic
/
size-zero-01
set-basic
/
In-empty
set-basic
/
In-insert
nat-basic
/
c
nat-basic
/
a
nat-basic
/
oz
set-basic
/
Size-insert
nat-basic
/
s-04
nat-basic
/
refl-nat
set-basic
/
ne-01