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Proof step 74 from proof cyclic-pseq (previous step)

¬ ( validrefs(str, (st[r2 -- fs '] .refval ' + refs) + r2 ', st[st[r2 -- fs '] .refval -- _type] .type, st) ∧ st[r2 -- fs '] .refval = st[r2 -- fs '] .refval ∧ is_referencevalue(st[r2 -- fs ']) ∧ is_obj(str, r2, st) ∧ fs ' ∈ instfields(st[r2 -- _type] .type .class) ∧ st[st[r2 -- fs '] .refval -- _type] .type ≤ fs .type ∧ is_valid_ref(str, st[r2 -- fs '] .refval, st) ∧ type∃(str, st[st[r2 -- fs '] .refval -- _type] .type)), st1[r1 -- _type] .type = mkclasstype(class), st[r2 -- _type] = st1[r1 -- _type], ps=(st[r2 -- fs '] .refval, st, st1[r1 -- fs '] .refval, st1), validrefs(str, (st[r2 -- fs '] .refval ' + refs) + r2 ', fs .type, st), is_obj(str, r2, st), is_obj(str, r1, st1), fs ' ∈ instfields(class), is_referencevalue(st[r2 -- fs ']), validrefs(str, st[r2 -- fs '] .refval ' + refs + r2 ', st[st[r2 -- fs '] .refval -- _type] .type, st), ∀ 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 = st[r2 -- fs '] .refval, r2 = jvmref, r1 = jvmref, validrefs(str, (st[r2 -- fs '] .refval ' + refs) + r2 ' + st[r2 -- fs '] .refval ', st[st[r2 -- fs '] .refval -- _type] .type, st), st[r2 -- fs '] .refval ∈ refs, dups(refs), r2 ∈ refs, cyclic(str, r1, st1), junkref(str, r1, st1), junkref(str, r2, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 73:
st[r2 -- _type] = st1[r1 -- _type], st1[r1 -- _type] .type = mkclasstype(class), is_valid_ref(str, st[r2 -- fs '] .refval, st), validrefs(str, st[r2 -- fs '] .refval ' + refs + r2 ', st[st[r2 -- fs '] .refval -- _type] .type, st), is_referencevalue(st[r2 -- fs ']), fs ' ∈ instfields(class), is_obj(str, r1, st1), is_obj(str, r2, st), validrefs(str, (st[r2 -- fs '] .refval ' + refs) + r2 ', fs .type, st), 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)) ⊦ r1 = jvmref, r2 = jvmref, r2 = st[r2 -- fs '] .refval, junkref(str, r2, st), junkref(str, r1, st1), cyclic(str, r1, st1), r2 ∈ refs, dups(refs), st[r2 -- fs '] .refval ∈ refs, validrefs(str, (st[r2 -- fs '] .refval ' + refs) + r2 ' + st[r2 -- fs '] .refval ', st[st[r2 -- fs '] .refval -- _type] .type, st), type∃(str, st[st[r2 -- fs '] .refval -- _type] .type) ∧ st[st[r2 -- fs '] .refval -- _type] .type ≤ fs .type

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ mkclasstype(class) .class = class], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ ¬ is_valid_ref(str, r, st) → ( validrefs (str, r ' + refs, ty, st) ↔ r = jvmref ∧ refs = [])], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]