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Proof step 39 from proof validrefs-subset-equiv (previous step)

is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty, is_obj(str, r, st0), st ⊆ st0, is_valid_ref(str, r, st), st0[r -- _type] .type ≤ ty, refs = [] ∨ mkfs(class, ty0, fieldvar) ' ∈ instfields(st0[r -- _type] .type .class) ∧ is_referencevalue(st0[r -- mkfs(class, ty0, fieldvar) ']) ∧ refs .first = st0[r -- mkfs(class, ty0, fieldvar) '] .refval ∧ validrefs(str, refs, ty0, st0), ∀ st, st0, ty, r, str, refs0. # refs0 < # refs → (validrefs(str, r ' + refs0, ty, st0) ∧ st ⊆ st0 ∧ validref(str, r, st[r -- _type] .type, st) → validrefs(str, r ' + refs0, ty, st)) ⊦ r = jvmref, junkref(str, r, st), refs = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ refs .first = st[r -- fs '] .refval ∧ validrefs(str, refs, fs .type, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 38:
refs .first = st0[r -- mkfs(class, ty0, fieldvar) '] .refval, is_obj(str, r, st), st[r -- _type] .type ≤ ty, st ⊆ st0, st0[r -- _type] .type ≤ ty, mkfs(class, ty0, fieldvar) ' ∈ instfields(st0[r -- _type] .type .class), is_referencevalue(st0[r -- mkfs(class, ty0, fieldvar) ']), validrefs(str, refs, ty0, st0), ∀ st, st0, ty, r, str, refs0. # refs0 < # refs → (validrefs(str, r ' + refs0, ty, st0) ∧ st ⊆ st0 ∧ validref(str, r, st[r -- _type] .type, st) → validrefs(str, r ' + refs0, ty, st)) ⊦ r = jvmref, refs = [], junkref(str, r, st), ∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ refs .first = st[r -- fs '] .refval ∧ validrefs(str, refs, fs .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_obj(str, r, st) → is_valid_ref(str, r, st)], [CSIMPSEQ : ⊦ st ⊆ st1 ∧ is_obj(str, r, st) → is_obj(str, r, st1)])]]