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Proof step 57 from proof hasSharing-pathex (previous step)

hasSharing(r0, st), validrefs(str, r ' + refs1 + r0 ', st[r -- _type] .type, st), ∀ st, r, str, refs. # refs < # (refs1 + r0 ') → (validrefs(str, r ' + refs, st[r -- _type] .type, st) ∧ hasSharing(refs .last, st) → refs = [] ∨ hasSharing(r, st)) ⊦ hasSharing(r, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ ty) → ¬ validrefs(str, r ' + refs, ty, st)
Proof step 56:
¬ (r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ st[r -- _type] .type)), hasSharing(r0, st), validrefs(str, r ' + refs1 + r0 ', st[r -- _type] .type, st), ∀ st, r, str, refs. # refs < # (refs1 + r0 ') → (validrefs(str, r ' + refs, st[r -- _type] .type, st) ∧ hasSharing(refs .last, st) → refs = [] ∨ hasSharing(r, st)) ⊦ hasSharing(r, st)

Rule argument

[speclemmaarg: , r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ ty) → ¬ validrefs(str, r ' + refs, ty, st) ,[st, ty, refs, r, str] → [st, st[r -- _type] .type, refs1 + r0 ', r, str] ,F ,cyclic , ,validrefs-is-junk ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, st[r -- _type] .type, refs1 + r0 ', r, str)]]