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Proof step 210 from proof cyclic-pseq (previous step)

(refs0 + r0 ') .first = st[r2 -- i '] .refval, st[r2 -- _length] .intval = st1[r1 -- _length] .intval, st[r2 -- _type] = st1[r1 -- _type], cyclic(str, st1[r1 -- i '] .refval, st1), 0 < st1[r1 -- _length] .intval, 0 ≤ i, validrefs(str, refs0 + r0 ', st1[r1 -- _type] .type .type, st), is_referencevalue(st[r2 -- i ']), i < st1[r1 -- _length] .intval, is_array(str, r1, st1), is_array(str, r2, st), is_arraytype(st1[r1 -- _type] .type), ps=((refs0 + r0 ') .first, st, st1[r1 -- i '] .refval, st1), is_referencevalue(st1[r1 -- i ']), ∀ 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)) ⊦ is_reftype(st1[r1 -- _type] .type .type), r1 = jvmref, r2 = jvmref, r2 ∈ refs0, dups(refs0), cyclic(str, r1, st1), r0 ≠ r2 ∧ ¬ r0 ∈ refs0, (refs0 + r0 ') .first ≠ jvmref ∧ (¬ st[(refs0 + r0 ') .first -- _type] .type ≤ st1[r1 -- _type] .type .type ∨ junkref(str, (refs0 + r0 ') .first, st)), (¬ st1[st1[r1 -- i '] .refval -- _type] .type ≤ st1[r1 -- _type] .type .type ∨ junkref(str, st1[r1 -- i '] .refval, st1)) ∧ st1[r1 -- i '] .refval ≠ jvmref, is_reftype(st1[r1 -- _type] .type .type) ∧ st1[st1[r1 -- i '] .refval -- _type] .type ≤ st1[r1 -- _type] .type .type

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 209:
(refs0 + r0 ') .first = st[r2 -- i '] .refval, st[r2 -- _length] .intval = st1[r1 -- _length] .intval, st[r2 -- _type] = st1[r1 -- _type], cyclic(str, st1[r1 -- i '] .refval, st1), 0 < st1[r1 -- _length] .intval, 0 ≤ i, validrefs(str, refs0 + r0 ', st1[r1 -- _type] .type .type, st), is_referencevalue(st[r2 -- i ']), i < st1[r1 -- _length] .intval, is_array(str, r1, st1), is_array(str, r2, st), is_arraytype(st1[r1 -- _type] .type), ps=((refs0 + r0 ') .first, st, st1[r1 -- i '] .refval, st1), is_referencevalue(st1[r1 -- i ']), ∀ 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)) ⊦ r1 = jvmref, r2 = jvmref, is_reftype(st1[r1 -- _type] .type .type), r2 ∈ refs0, dups(refs0), cyclic(str, r1, st1), r0 ≠ r2 ∧ ¬ r0 ∈ refs0, (refs0 + r0 ') .first ≠ jvmref ∧ (st[(refs0 + r0 ') .first -- _type] .type ≠ st1[r1 -- _type] .type .type ∨ junkref(str, (refs0 + r0 ') .first, st)), (st1[st1[r1 -- i '] .refval -- _type] .type ≠ st1[r1 -- _type] .type .type ∨ junkref(str, st1[r1 -- i '] .refval, st1)) ∧ st1[r1 -- i '] .refval ≠ jvmref

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_reftype(ty0) → (ty ≤ ty0 ↔ ty = ty0)])]]