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Proof step 205 from proof pseq-subset (previous step)

st[r -- _type] = st1[r1 -- _type], st2[r -- _type] = st1[r1 -- _type], r ∈ st2, r ∈ st, r -- _type ∈ st2, r -- _type ∈ st, is_arraytype(st1[r1 -- _type] .type) → st[r -- _length] .intval = st1[r1 -- _length] .intval ∧ (∀ i. ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i ∧ is_referencevalue(st[r -- i ']) → ps=(st[r -- i '] .refval, st, st1[r1 -- i '] .refval, st1)) ∧ (∀ i. ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i ∧ ¬ is_referencevalue(st[r -- i ']) → st[r -- i '] = st1[r1 -- i ']), is_classtype(st1[r1 -- _type] .type) → (∀ fs. fs ' ∈ instfields(st1[r1 -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) → ps=(st[r -- fs '] .refval, st, st1[r1 -- fs '] .refval, st1)) ∧ (∀ fs. fs ' ∈ instfields(st1[r1 -- _type] .type .class) ∧ ¬ is_referencevalue(st[r -- fs ']) → st[r -- fs '] = st1[r1 -- fs ']), ∀ rk. rk ∈ st → rk ∈ st2 ∧ st[rk] = st2[rk], ∀ st1, r1, st2, st0, r0, str0. maxpath(str0, r0, st0) < maxpath(str, r, st) → ( st0 ⊆ st2 ∧ ps=(r0, st0, r1, st1) → junkref(str0, r0, st0) ∨ cyclic(str0, r0, st0) ∨ junkref(str0, r1, st1) ∨ cyclic(str0, r1, st1) ∨ ps=(r0, st2, r1, st1)) ⊦ is_arraytype(st1[r1 -- _type] .type) → st2[r -- _length] .intval = st1[r1 -- _length] .intval ∧ (0 ≤ i ∧ i < st2[r -- _length] .intval ∧ is_referencevalue(st2[r -- i ']) → ps=(st2[r -- i '] .refval, st2, st1[r1 -- i '] .refval, st1)) ∧ (0 ≤ i0 ∧ i0 < st2[r -- _length] .intval ∧ ¬ is_referencevalue(st2[r -- i0 ']) → st2[r -- i0 '] = st1[r1 -- i0 ']), r = jvmref, r1 = jvmref, junkref(str, r, st), cyclic(str, r, st), junkref(str, r1, st1), cyclic(str, r1, st1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 204:
st[r -- _type] = st1[r1 -- _type], st2[r -- _type] = st1[r1 -- _type], st[r -- _length] .intval = st1[r1 -- _length] .intval, is_arraytype(st1[r1 -- _type] .type), r ∈ st2, r ∈ st, r -- _type ∈ st2, r -- _type ∈ st, ∀ rk. rk ∈ st → rk ∈ st2 ∧ st[rk] = st2[rk], ∀ i. ¬ i < 0 ∧ ¬ st1[r1 -- _length] .intval ≤ i ∧ is_referencevalue(st[r -- i ']) → ps=(st[r -- i '] .refval, st, st1[r1 -- i '] .refval, st1), ∀ i. ¬ i < 0 ∧ ¬ st1[r1 -- _length] .intval ≤ i ∧ ¬ is_referencevalue(st[r -- i ']) → st[r -- i '] = st1[r1 -- i '], ∀ st1, r1, st2, st0, r0, str0. maxpath(str0, r0, st0) < maxpath(str, r, st) → ( st0 ⊆ st2 ∧ ps=(r0, st0, r1, st1) → junkref(str0, r0, st0) ∨ cyclic(str0, r0, st0) ∨ junkref(str0, r1, st1) ∨ cyclic(str0, r1, st1) ∨ ps=(r0, st2, r1, st1)) ⊦ r = jvmref, r1 = jvmref, junkref(str, r, st), cyclic(str, r, st), junkref(str, r1, st1), cyclic(str, r1, st1), st2[r -- _length] .intval = st1[r1 -- _length] .intval ∧ (0 ≤ i ∧ i < st2[r -- _length] .intval ∧ is_referencevalue(st2[r -- i ']) → ps=(st2[r -- i '] .refval, st2, st1[r1 -- i '] .refval, st1)) ∧ (0 ≤ i0 ∧ i0 < st2[r -- _length] .intval ∧ ¬ is_referencevalue(st2[r -- i0 ']) → st2[r -- i0 '] = st1[r1 -- i0 '])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_arraytype(ty) → ¬ is_classtype(ty)])]]