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Theorem ll-trav1-end
r1 ≠ null ⊦ h[r1] = a × null → (((ll-trav(r0, r1, x) * hP))(h) ↔ x ≠ [] ∧ (∃ y. x = y + a ∧ ((lls(r0, r1, y) * r1 => a × null * hP))(h)))
Type: A user defined theorem
Validity: The proof is valid.
Features: as,
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
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the proof
Infos about the proof
Proved?: Yes
Interactions: 2
Proof steps: 9
Used lemmas:
lls-one
,
lls-null
,
lls-rec
,
lls-base
,
ll-trav1-def
,
Used spec theorems:
Used simplifier rules:
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heap-sep
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sep-com
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sep-ass
heap-sep
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false-rev
heap-sep
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false-and
heap-sep
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and-ass
heap-sep
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and-com
heap-sep
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false-sep
heap-sep
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falseH
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e-03
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e-01
maplet
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ex1-shift
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cell
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inj-tim
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c
heap-sep
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true-rev
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true-and
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emp-sep
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prop-shift
heap-sep
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heap-sep
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e-02