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Proof step 41 from proof cyclic-pseq (previous step)

r2 = st[r2 -- fs '] .refval, st1[r1 -- _type] .type = mkclasstype(class), st[r2 -- _type] = st1[r1 -- _type], is_referencevalue(st1[r1 -- fs ']), cyclic(str, st1[r1 -- fs '] .refval, st1), 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), junkref(str, st1[r1 -- fs '] .refval, st1), is_reftype(fs .type) ∧ st1[st1[r1 -- fs '] .refval -- _type] .type ≤ fs .type

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 35:
⊦ validrefs(str, r ', ty, st) ↔ r = jvmref ∨ r ≠ jvmref ∧ is_valid_ref(str, r, st) ∧ st[r -- _type] .type ≤ ty
Proof step 40:
r2 = st[r2 -- fs '] .refval, st1[r1 -- _type] .type = mkclasstype(class), st[r2 -- _type] = st1[r1 -- _type], is_referencevalue(st1[r1 -- fs ']), cyclic(str, st1[r1 -- fs '] .refval, st1), r2 = jvmref ∨ r2 ≠ jvmref ∧ is_valid_ref(str, r2, st) ∧ st[r2 -- _type] .type ≤ fs .type, 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), junkref(str, st1[r1 -- fs '] .refval, st1), is_reftype(fs .type) ∧ st1[st1[r1 -- fs '] .refval -- _type] .type ≤ fs .type

Rule argument

[speclemmaarg: , validrefs(str, r ', ty, st) ↔ r = jvmref ∨ r ≠ jvmref ∧ is_valid_ref(str, r, st) ∧ st[r -- _type] .type ≤ ty ,[st, ty, r, str] → [st, fs .type, r2, str] ,F ,cyclic , ,validrefs-one ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, fs .type, r2, str)]]