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Proof step 188 from proof cyclic-pseq (previous step)

st[r2 -- _type] = st1[r1 -- _type], st[r2 -- _length] .intval = st1[r1 -- _length] .intval, 0 ≤ i, 0 < st1[r1 -- _length] .intval, ps=(st[r2 -- i '] .refval, st, st1[r1 -- i '] .refval, st1), is_arraytype(st1[r1 -- _type] .type), is_array(str, r2, st), is_array(str, r1, st1), i < st1[r1 -- _length] .intval, is_referencevalue(st[r2 -- i ']), validrefs(str, (st[r2 -- i '] .refval ' + refs) + r0 ', st1[r1 -- _type] .type .type, st), ∀ i. ¬ i < 0 ∧ ¬ st1[r1 -- _length] .intval ≤ i ∧ ¬ is_referencevalue(st[r2 -- i ']) → st[r2 -- i '] = st1[r1 -- i '], ∀ st, r, st0, r0, str0. maxpath(str0, r0, st0) < maxpath(str, r1, st1) → (ps=(r, st, r0, st0) ∧ cyclic(str0, r, st) → junkref(str0, r, st) ∨ junkref(str0, r0, st0) ∨ cyclic(str0, r0, st0)) ⊦ r2 = jvmref, r1 = jvmref, r2 = st[r2 -- i '] .refval, r0 ∈ refs, cyclic(str, r1, st1), junkref(str, r1, st1), junkref(str, r2, st), dups(refs), st[r2 -- i '] .refval ∈ refs, r2 ∈ refs, ∃ refs. dups(refs) ∧ refs .first = st[r2 -- i '] .refval ∧ validrefs(str, refs, st[st[r2 -- i '] .refval -- _type] .type, st), r0 ≠ r2 ∧ r0 ≠ st[r2 -- i '] .refval

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 173:
⊦ ¬ validrefs(str, r ' + refs, st[r -- _type] .type, st) → ¬ validrefs(str, r ' + refs, ty, st)
Proof step 187:
¬ ¬ validrefs(str, st[r2 -- i '] .refval ' + refs + r0 ', st[st[r2 -- i '] .refval -- _type] .type, st), st[r2 -- _type] = st1[r1 -- _type], st[r2 -- _length] .intval = st1[r1 -- _length] .intval, 0 ≤ i, 0 < st1[r1 -- _length] .intval, ps=(st[r2 -- i '] .refval, st, st1[r1 -- i '] .refval, st1), is_arraytype(st1[r1 -- _type] .type), is_array(str, r2, st), is_array(str, r1, st1), i < st1[r1 -- _length] .intval, is_referencevalue(st[r2 -- i ']), validrefs(str, (st[r2 -- i '] .refval ' + refs) + r0 ', st1[r1 -- _type] .type .type, st), ∀ i. ¬ i < 0 ∧ ¬ st1[r1 -- _length] .intval ≤ i ∧ ¬ is_referencevalue(st[r2 -- i ']) → st[r2 -- i '] = st1[r1 -- i '], ∀ st, r, st0, r0, str0. maxpath(str0, r0, st0) < maxpath(str, r1, st1) → (ps=(r, st, r0, st0) ∧ cyclic(str0, r, st) → junkref(str0, r, st) ∨ junkref(str0, r0, st0) ∨ cyclic(str0, r0, st0)) ⊦ r2 = jvmref, r1 = jvmref, r2 = st[r2 -- i '] .refval, r0 ∈ refs, cyclic(str, r1, st1), junkref(str, r1, st1), junkref(str, r2, st), dups(refs), st[r2 -- i '] .refval ∈ refs, r2 ∈ refs, ∃ refs. dups(refs) ∧ refs .first = st[r2 -- i '] .refval ∧ validrefs(str, refs, st[st[r2 -- i '] .refval -- _type] .type, st), r0 ≠ r2 ∧ r0 ≠ st[r2 -- i '] .refval

Rule argument

[speclemmaarg: , ¬ validrefs(str, r ' + refs, st[r -- _type] .type, st) → ¬ validrefs(str, r ' + refs, ty, st) ,[st, ty, refs, r, str] → [st, st1[r1 -- _type] .type .type, refs + r0 ', st[r2 -- i '] .refval, str] ,F ,cyclic , ,validrefs-sametype ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st, st1[r1 -- _type] .type .type, refs + r0 ', st[r2 -- i '] .refval, str)]]