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Proof step 49 from proof cyclic-pseq (previous step)

r2 = st[r2 -- fs '] .refval, st1[r1 -- _type] .type = mkclasstype(class), st[r2 -- _type] = st1[r1 -- _type], validrefs(str, r2 ', fs .type, st), is_obj(str, r2, st), is_obj(str, r1, st1), fs ' ∈ instfields(class), is_referencevalue(st[r2 -- fs ']), ps=(r2, 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)

User applied rule apply induction

And obtained the following new goals

Proof step 21:
r2 = st[r2 -- fs '] .refval, st1[r1 -- _type] .type = mkclasstype(class), st[r2 -- _type] = st1[r1 -- _type], validrefs(str, r2 ', fs .type, st), is_obj(str, r2, st), is_obj(str, r1, st1), fs ' ∈ instfields(class), is_referencevalue(st[r2 -- fs ']), ps=(r2, 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)) ⊦ maxpath(str, st1[r1 -- fs '] .refval, st1) < maxpath(str, r1, st1), r2 = jvmref, r1 = jvmref, cyclic(str, r1, st1), junkref(str, r1, st1), junkref(str, r2, st)
Proof step 27:
r2 = st[r2 -- fs '] .refval, st1[r1 -- _type] .type = mkclasstype(class), st[r2 -- _type] = st1[r1 -- _type], validrefs(str, r2 ', fs .type, st), is_obj(str, r2, st), is_obj(str, r1, st1), fs ' ∈ instfields(class), is_referencevalue(st[r2 -- fs ']), ps=(r2, 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)) ⊦ ps=(st[r2 -- fs '] .refval, st, st1[r1 -- fs '] .refval, st1) ∧ cyclic(str, st[r2 -- fs '] .refval, st), r2 = jvmref, r1 = jvmref, cyclic(str, r1, st1), junkref(str, r1, st1), junkref(str, r2, st)
Proof step 48:
junkref(str, st[r2 -- fs '] .refval, st) ∨ junkref(str, st1[r1 -- fs '] .refval, st1) ∨ cyclic(str, st1[r1 -- fs '] .refval, st1), r2 = st[r2 -- fs '] .refval, st1[r1 -- _type] .type = mkclasstype(class), st[r2 -- _type] = st1[r1 -- _type], validrefs(str, r2 ', fs .type, st), is_obj(str, r2, st), is_obj(str, r1, st1), fs ' ∈ instfields(class), is_referencevalue(st[r2 -- fs ']), ps=(r2, 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)

Rule argument

[substlist-arg: [st, r, st0, r0, str0] → [st, st[r2 -- fs '] .refval, st1, st1[r1 -- fs '] .refval, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, st[r2 -- fs '] .refval, st1, st1[r1 -- fs '] .refval, str)]]