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Proof step 54 from proof validrefs-lastelem (previous step)

st[r0 -- mkfs(class, ty0, fieldvar) '] = refval(r1), st[r0 -- mkfs(class0, ty1, fieldvar0) '] = refval(r1), is_obj(str, r0, st), st[r0 -- _type] .type ≤ ty, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class), validrefs(str, r1 ' + refs0 + r ', ty0, st), mkfs(class0, ty1, fieldvar0) ' ∈ instfields(st[r0 -- _type] .type .class), validrefs(str, r1 ' + refs0, ty1, st), is_valid_ref(str, r1, st), st[r1 -- _type] .type ≤ ty0, st[r1 -- _type] .type ≤ ty1 ⊦ r0 = jvmref, r1 = jvmref, has_reffield((r1 ' + refs0) .last, st), validrefs(str, r1 ' + refs0, ty0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 28:
⊦ is_valid_ref(str, r, st) ↔ is_obj(str, r, st) ∨ is_array(str, r, st)
Proof step 53:
st[r0 -- mkfs(class, ty0, fieldvar) '] = refval(r1), st[r0 -- mkfs(class0, ty1, fieldvar0) '] = refval(r1), is_obj(str, r0, st), st[r0 -- _type] .type ≤ ty, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class), validrefs(str, r1 ' + refs0 + r ', ty0, st), mkfs(class0, ty1, fieldvar0) ' ∈ instfields(st[r0 -- _type] .type .class), validrefs(str, r1 ' + refs0, ty1, st), is_obj(str, r1, st) ∨ is_array(str, r1, st), st[r1 -- _type] .type ≤ ty0, st[r1 -- _type] .type ≤ ty1 ⊦ r0 = jvmref, r1 = jvmref, has_reffield((r1 ' + refs0) .last, st), validrefs(str, r1 ' + refs0, ty0, st)

Rule argument

[speclemmaarg: ,is_valid_ref(str, r, st) ↔ is_obj(str, r, st) ∨ is_array(str, r, st) ,[st, r, str] → [st, r1, str] ,F ,addfuns , ,is-valid-ref-stronger-def ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, r1, str)]]