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Proof step 137 from proof validref-refs-last-valid-subset (previous step)

acc + r1 ' = r2 ' + refs, st0[r0 -- mkfs(class, ty0, fieldvar) '] = refval(r2), is_obj(str, r0, st0), validref(str, r0, st[r0 -- _type] .type, st), st ⊆ st0, st0[r0 -- _type] .type ≤ ty, mkfs(class, ty0, fieldvar) ' ∈ instfields(st0[r0 -- _type] .type .class), validrefs(str, r2 ' + refs, ty0, st0), ∀ str, r, st, st0, r1, ty. validref(str, r, st[r -- _type] .type, st) ∧ st ⊆ st0 ∧ r ∈ acc ∧ validrefs(str, acc + r1 ', ty, st0) → validref(str, r1, st[r1 -- _type] .type, st) ⊦ r0 = jvmref, validref(str, r1, st[r1 -- _type] .type, st), r1 ≠ r2 ∧ ¬ r1 ∈ refs, ¬ r2 ∈ acc ∧ r2 ≠ r1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 86:
⊦ rk ∈ st ∧ st[rk] ≠ st1[rk] → ¬ st ⊆ st1
Proof step 136:
¬ (r0 -- _type ∈ st ∧ st[r0 -- _type] ≠ st0[r0 -- _type]), acc + r1 ' = r2 ' + refs, st0[r0 -- mkfs(class, ty0, fieldvar) '] = refval(r2), is_obj(str, r0, st0), validref(str, r0, st[r0 -- _type] .type, st), st ⊆ st0, st0[r0 -- _type] .type ≤ ty, mkfs(class, ty0, fieldvar) ' ∈ instfields(st0[r0 -- _type] .type .class), validrefs(str, r2 ' + refs, ty0, st0), ∀ str, r, st, st0, r1, ty. validref(str, r, st[r -- _type] .type, st) ∧ st ⊆ st0 ∧ r ∈ acc ∧ validrefs(str, acc + r1 ', ty, st0) → validref(str, r1, st[r1 -- _type] .type, st) ⊦ r0 = jvmref, validref(str, r1, st[r1 -- _type] .type, st), r1 ≠ r2 ∧ ¬ r1 ∈ refs, ¬ r2 ∈ acc ∧ r2 ≠ r1

Rule argument

[speclemmaarg: ,rk ∈ st ∧ st[rk] ≠ st1[rk] → ¬ st ⊆ st1 ,[rk, st1, st] → [r0 -- _type, st0, st] ,F ,store ,javastore-ostorea ,subset-elem-eq-01 ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (r0 -- _type, st0, st)]]