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Proof step 160 from proof cyclic-pseq (previous step)

is_array(str, r2, st) ∧ st[r2 -- _type] .type ≤ st1[r1 -- _type] .type, r2 = st[r2 -- i '] .refval, st[r2 -- _length] .intval = st1[r1 -- _length] .intval, st[r2 -- _type] = st1[r1 -- _type], validrefs(str, r2 ', 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=(r2, st, st1[r1 -- i '] .refval, st1), 0 < st1[r1 -- _length] .intval, 0 ≤ 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, junkref(str, r2, st), junkref(str, r1, st1), cyclic(str, r1, st1), r2 ' = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r2 -- _length] .intval ∧ is_referencevalue(st[r2 -- i ']) ∧ r2 ' .first = st[r2 -- i '] .refval ∧ validrefs(str, r2 ', st[r2 -- _type] .type .type, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 159:
st[r2 -- _type] = st1[r1 -- _type], st[r2 -- _length] .intval = st1[r1 -- _length] .intval, r2 = st[r2 -- i '] .refval, 0 ≤ i, 0 < st1[r1 -- _length] .intval, ps=(r2, 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, r2 ', 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, cyclic(str, r1, st1), junkref(str, r1, st1), junkref(str, r2, st), ∃ i0. ¬ i0 < 0 ∧ ¬ st1[r1 -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r2 -- i0 ']) ∧ r2 = st[r2 -- i0 '] .refval

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ty ≤ ty], [CSIMPSEQ : ⊦ r ' .first = r], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ r ' ≠ []])]]