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Proof step 24 from proof validrefs-subset (previous step)

r0 -- mkfs(class, ty1, fieldvar) ' ∈ st, st[r0 -- _type] = st0[r0 -- _type], st0[r0 -- mkfs(class, ty1, fieldvar) '] = refval(r), r0 ∈ st0, r0 ∈ st, r0 -- _type ∈ st0, r0 -- _type ∈ st, is_obj(str, r0, st), is_valid_ref(str, r0, st0), st0[r0 -- _type] .type ≤ ty, mkfs(class, ty1, fieldvar) ' ∈ instfields(st0[r0 -- _type] .type .class), validrefs(str, r ' + refs, ty1, st0), ∀ str0, ty0, st1, st2. validrefs(str0, r ' + refs, ty0, st1) ∧ st2 ⊆ st1 ∧ ¬ junkref(str0, r, st2) → validrefs(str0, r ' + refs, ty0, st2), r0 -- mkfs(class, ty1, fieldvar) ' ∈ st → r0 -- mkfs(class, ty1, fieldvar) ' ∈ st0 ∧ st[r0 -- mkfs(class, ty1, fieldvar) '] = refval(r), ∀ rk. rk ∈ st → rk ∈ st0 ∧ st[rk] = st0[rk] ⊦ r0 = jvmref, junkref(str, r0, st), is_referencevalue(st[r0 -- mkfs(class, ty1, fieldvar) ']) ∧ r = st[r0 -- mkfs(class, ty1, fieldvar) '] .refval ∧ validrefs(str, st[r0 -- mkfs(class, ty1, fieldvar) '] .refval ' + refs, ty1, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
st[r0 -- mkfs(class, ty1, fieldvar) '] = refval(r), st0[r0 -- mkfs(class, ty1, fieldvar) '] = refval(r), st[r0 -- _type] = st0[r0 -- _type], r0 -- mkfs(class, ty1, fieldvar) ' ∈ st0, validrefs(str, r ' + refs, ty1, st0), mkfs(class, ty1, fieldvar) ' ∈ instfields(st0[r0 -- _type] .type .class), st0[r0 -- _type] .type ≤ ty, is_valid_ref(str, r0, st0), is_obj(str, r0, st), r0 -- _type ∈ st, r0 -- _type ∈ st0, r0 ∈ st, r0 ∈ st0, r0 -- mkfs(class, ty1, fieldvar) ' ∈ st, ∀ str0, ty0, st1, st2. validrefs(str0, r ' + refs, ty0, st1) ∧ st2 ⊆ st1 ∧ ¬ junkref(str0, r, st2) → validrefs(str0, r ' + refs, ty0, st2), ∀ rk. rk ∈ st → rk ∈ st0 ∧ st[rk] = st0[rk] ⊦ r0 = jvmref, junkref(str, r0, st), validrefs(str, r ' + refs, ty1, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]