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Proof step 29 from proof pseq-subset (previous step)

st[r -- fs '] = refval(r2), st2[r -- fs '] = refval(r2), st1[r1 -- _type] .type = mkclasstype(class), st[r -- _type] = st1[r1 -- _type], st2[r -- _type] = st1[r1 -- _type], st[r2 -- _type] .type ≤ fs .type, is_reftype(fs .type), is_obj(str, r, st), is_obj(str, r1, st1), r ∈ st2, r ∈ st, r -- _type ∈ st2, r -- _type ∈ st, fs ' ∈ instfields(class), r -- fs ' ∈ st2, r -- fs ' ∈ st, ps=(r2, st, st1[r1 -- fs '] .refval, st1), junkref(str, st1[r1 -- fs '] .refval, st1) ∨ cyclic(str, st1[r1 -- fs '] .refval, st1), ∀ fs. fs ' ∈ instfields(class) ∧ is_referencevalue(st[r -- fs ']) → ps=(st[r -- fs '] .refval, st, st1[r1 -- fs '] .refval, st1), ∀ fs. fs ' ∈ instfields(class) ∧ ¬ is_referencevalue(st[r -- fs ']) → st[r -- fs '] = st1[r1 -- fs '], ∀ rk. rk ∈ st → rk ∈ st2 ∧ st[rk] = st2[rk], ∀ st1, r1, st2, st0, r0, str0. maxpath(str0, r0, st0) < maxpath(str, r, st) → ( st0 ⊆ st2 ∧ ps=(r0, st0, r1, st1) → junkref(str0, r0, st0) ∨ cyclic(str0, r0, st0) ∨ junkref(str0, r1, st1) ∨ cyclic(str0, r1, st1) ∨ ps=(r0, st2, r1, st1)) ⊦ r2 = jvmref, r = jvmref, r1 = jvmref, cyclic(str, r2, st), junkref(str, r2, st), cyclic(str, r, st), junkref(str, r1, st1), cyclic(str, r1, st1), ps=(r2, st2, st1[r1 -- fs '] .refval, st1), cyclic(str, st1[r1 -- fs '] .refval, st1) ∧ st1[r1 -- fs '] = refval(st1[r1 -- fs '] .refval) ∧ st1[st1[r1 -- fs '] .refval -- _type] .type ≤ fs .type

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ is_referencevalue(val) → refval(val .refval) = val
Proof step 28:
is_referencevalue(st1[r1 -- fs ']), st[r -- fs '] = refval(r2), st2[r -- fs '] = refval(r2), st1[r1 -- _type] .type = mkclasstype(class), st[r -- _type] = st1[r1 -- _type], st2[r -- _type] = st1[r1 -- _type], st[r2 -- _type] .type ≤ fs .type, is_reftype(fs .type), is_obj(str, r, st), is_obj(str, r1, st1), r ∈ st2, r ∈ st, r -- _type ∈ st2, r -- _type ∈ st, fs ' ∈ instfields(class), r -- fs ' ∈ st2, r -- fs ' ∈ st, ps=(r2, st, st1[r1 -- fs '] .refval, st1), junkref(str, st1[r1 -- fs '] .refval, st1) ∨ cyclic(str, st1[r1 -- fs '] .refval, st1), ∀ fs. fs ' ∈ instfields(class) ∧ is_referencevalue(st[r -- fs ']) → ps=(st[r -- fs '] .refval, st, st1[r1 -- fs '] .refval, st1), ∀ fs. fs ' ∈ instfields(class) ∧ ¬ is_referencevalue(st[r -- fs ']) → st[r -- fs '] = st1[r1 -- fs '], ∀ rk. rk ∈ st → rk ∈ st2 ∧ st[rk] = st2[rk], ∀ st1, r1, st2, st0, r0, str0. maxpath(str0, r0, st0) < maxpath(str, r, st) → ( st0 ⊆ st2 ∧ ps=(r0, st0, r1, st1) → junkref(str0, r0, st0) ∨ cyclic(str0, r0, st0) ∨ junkref(str0, r1, st1) ∨ cyclic(str0, r1, st1) ∨ ps=(r0, st2, r1, st1)) ⊦ r2 = jvmref, r = jvmref, r1 = jvmref, cyclic(str, r2, st), junkref(str, r2, st), cyclic(str, r, st), junkref(str, r1, st1), cyclic(str, r1, st1), ps=(r2, st2, st1[r1 -- fs '] .refval, st1), cyclic(str, st1[r1 -- fs '] .refval, st1) ∧ st1[r1 -- fs '] = st1[r1 -- fs '] ∧ st1[st1[r1 -- fs '] .refval -- _type] .type ≤ fs .type

Rule argument

[speclemmaarg: ,is_referencevalue(val) → refval(val .refval) = val ,[val] → [st1[r1 -- fs ']] ,F ,javavalue , ,refva-sel ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_referencevalue (st[r -- fs ']) ∧ is_reftype(fs .type) ∧ fs ' ∈ instfields(class) ∧ st[r -- _type] .type = mkclasstype(class) → ¬ is_obj(str, r, st)])], [EXTRATERMS : (st1[r1 -- fs '])]]