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Proof step 179 from proof cyclic-pseq (previous step)

¬ ( validrefs(str, (st[r2 -- i '] .refval ' + refs) + r2 ', st[st[r2 -- i '] .refval -- _type] .type, st) ∧ st[r2 -- i '] .refval = st[r2 -- i '] .refval ∧ is_array(str, r2, st) ∧ 0 ≤ i ∧ i < st[r2 -- _length] .intval ∧ st[st[r2 -- i '] .refval -- _type] .type ≤ st[r2 -- _type] .type .type ∧ is_valid_ref(str, st[r2 -- i '] .refval, st) ∧ type∃(str, st[st[r2 -- i '] .refval -- _type] .type)), st[r2 -- _type] = st1[r1 -- _type], st[r2 -- _length] .intval = st1[r1 -- _length] .intval, validrefs(str, st[r2 -- i '] .refval ' + refs + r2 ', st[st[r2 -- i '] .refval -- _type] .type, st), 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) + 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, r2 = st[r2 -- i '] .refval, cyclic(str, r1, st1), junkref(str, r1, st1), junkref(str, r2, st), dups(refs), st[r2 -- i '] .refval ∈ refs, r2 ∈ refs, validrefs(str, st[r2 -- i '] .refval ' + refs + r2 ' + st[r2 -- i '] .refval ', st[st[r2 -- i '] .refval -- _type] .type, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 178:
st[r2 -- _length] .intval = st1[r1 -- _length] .intval, st[r2 -- _type] = st1[r1 -- _type], is_valid_ref(str, st[r2 -- i '] .refval, st), validrefs(str, (st[r2 -- i '] .refval ' + refs) + 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=(st[r2 -- i '] .refval, st, st1[r1 -- i '] .refval, st1), 0 < st1[r1 -- _length] .intval, 0 ≤ i, validrefs(str, st[r2 -- i '] .refval ' + refs + r2 ', st[st[r2 -- i '] .refval -- _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 = st[r2 -- i '] .refval, r1 = jvmref, r2 = jvmref, validrefs(str, st[r2 -- i '] .refval ' + refs + r2 ' + st[r2 -- i '] .refval ', st[st[r2 -- i '] .refval -- _type] .type, st), r2 ∈ refs, st[r2 -- i '] .refval ∈ refs, dups(refs), junkref(str, r2, st), junkref(str, r1, st1), cyclic(str, r1, st1), type∃(str, st[st[r2 -- i '] .refval -- _type] .type) ∧ st[st[r2 -- i '] .refval -- _type] .type ≤ st1[r1 -- _type] .type .type

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ ¬ is_valid_ref(str, r, st) → ( validrefs (str, r ' + refs, ty, st) ↔ r = jvmref ∧ refs = [])], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]