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Proof step 237 from proof cyclic-pseq (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 236:
(refs0 + r0 ') .first = st[r2 -- i '] .refval, st[r2 -- _length] .intval = st1[r1 -- _length] .intval, st[r2 -- _type] = st1[r1 -- _type], 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), ∀ i. ¬ i < 0 ∧ ¬ st1[r1 -- _length] .intval ≤ i ∧ ¬ is_referencevalue(st[r2 -- i ']) → st[r2 -- i '] = st1[r1 -- i '], ∀ i. ¬ i < 0 ∧ ¬ st1[r1 -- _length] .intval ≤ i ∧ is_referencevalue(st[r2 -- i ']) → ps=(st[r2 -- i '] .refval, st, st1[r1 -- i '] .refval, st1), ∀ 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, r2 ∈ refs0, dups(refs0), junkref(str, r2, st), junkref(str, r1, st1), cyclic(str, r1, st1), r0 ≠ r2 ∧ ¬ r0 ∈ refs0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ty ≤ ty], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []])]]