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Proof step 129 from proof cyclic-pseq (previous step)

is_obj(str, r2, st) ∧ st[r2 -- _type] .type ≤ mkclasstype(class), st1[r1 -- _type] .type = mkclasstype(class), st[r2 -- _type] = st1[r1 -- _type], is_obj(str, r1, st1), refs0 + r0 ' = [] ∨ (∃ fs. fs ' ∈ instfields(st[r2 -- _type] .type .class) ∧ is_referencevalue(st[r2 -- fs ']) ∧ (refs0 + r0 ') .first = st[r2 -- fs '] .refval ∧ validrefs(str, refs0 + r0 ', fs .type, st)), is_valid_ref(str, r2, st), ∀ fs. fs ' ∈ instfields(class) ∧ is_referencevalue(st[r2 -- fs ']) → ps=(st[r2 -- fs '] .refval, st, st1[r1 -- fs '] .refval, st1), ∀ fs. fs ' ∈ instfields(class) ∧ ¬ is_referencevalue(st[r2 -- fs ']) → st[r2 -- fs '] = st1[r1 -- fs '], ∀ 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 128:
(refs0 + r0 ') .first = st[r2 -- fs '] .refval, st[r2 -- _type] = st1[r1 -- _type], st1[r1 -- _type] .type = mkclasstype(class), is_obj(str, r1, st1), is_obj(str, r2, st), validrefs(str, refs0 + r0 ', fs .type, st), is_referencevalue(st[r2 -- fs ']), fs ' ∈ instfields(class), ∀ fs. fs ' ∈ instfields(class) ∧ ¬ is_referencevalue(st[r2 -- fs ']) → st[r2 -- fs '] = st1[r1 -- fs '], ∀ fs. fs ' ∈ instfields(class) ∧ is_referencevalue(st[r2 -- fs ']) → ps=(st[r2 -- fs '] .refval, st, st1[r1 -- fs '] .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 : ⊦ class ≤ class], [CSIMPSEQ : ⊦ mkclasstype(class1) ≤ mkclasstype(class2) ↔ class1 ≤ class2], [CSIMPSEQ : ⊦ mkclasstype(class) .class = class], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ is_obj(str, r, st) → is_valid_ref(str, r, st)])]]