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Proof step 52 from proof junkrefs-union-disjoint (previous step)

¬ r -- _type ∈ st, st1 .refs ∩ st .refs = ∅, (st1 ∪ st)[r -- mkfs(class, ty0, fieldvar) '] = refval(r0), st1[r -- _type] .type ≤ ty, is_obj(str, r, st1), mkfs(class, ty0, fieldvar) ' ∈ instfields(st1[r -- _type] .type .class), junkrefs(str, r0 ' + acc, ty0, st1 ∪ st), r ∈ st1, st1[r -- _type] .type ≤ ty, ∀ st1, st, r, str, ty. st1 .refs ∩ st .refs = ∅ ∧ r ∈ st1 ∧ junkrefs(str, r ' + acc, ty, st1 ∪ st) → junkrefs(str, r ' + acc, ty, st1) ⊦ r = jvmref, ∃ fs0. fs0 ' ∈ instfields(st1[r -- _type] .type .class) ∧ is_referencevalue(st1[r -- fs0 ']) ∧ r0 = st1[r -- fs0 '] .refval ∧ junkrefs(str, st1[r -- fs0 '] .refval ' + acc, fs0 .type, st1), mkfs(class, ty0, fieldvar) ' ∈ instfields(st1[r -- _type] .type .class) ∧ is_referencevalue(st1[r -- mkfs(class, ty0, fieldvar) ']) ∧ r0 = st1[r -- mkfs(class, ty0, fieldvar) '] .refval ∧ junkrefs(str, st1[r -- mkfs(class, ty0, fieldvar) '] .refval ' + acc, ty0, st1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 41:
⊦ ¬ rk ∈ st0 → (st ∪ st0)[rk] = st[rk]
Proof step 47:
¬ ¬ r -- mkfs(class, ty0, fieldvar) ' ∈ st, ¬ r -- _type ∈ st, st1 .refs ∩ st .refs = ∅, (st1 ∪ st)[r -- mkfs(class, ty0, fieldvar) '] = refval(r0), st1[r -- _type] .type ≤ ty, is_obj(str, r, st1), mkfs(class, ty0, fieldvar) ' ∈ instfields(st1[r -- _type] .type .class), junkrefs(str, r0 ' + acc, ty0, st1 ∪ st), r ∈ st1, st1[r -- _type] .type ≤ ty, ∀ st1, st, r, str, ty. st1 .refs ∩ st .refs = ∅ ∧ r ∈ st1 ∧ junkrefs(str, r ' + acc, ty, st1 ∪ st) → junkrefs(str, r ' + acc, ty, st1) ⊦ r = jvmref, ∃ fs0. fs0 ' ∈ instfields(st1[r -- _type] .type .class) ∧ is_referencevalue(st1[r -- fs0 ']) ∧ r0 = st1[r -- fs0 '] .refval ∧ junkrefs(str, st1[r -- fs0 '] .refval ' + acc, fs0 .type, st1), mkfs(class, ty0, fieldvar) ' ∈ instfields(st1[r -- _type] .type .class) ∧ is_referencevalue(st1[r -- mkfs(class, ty0, fieldvar) ']) ∧ r0 = st1[r -- mkfs(class, ty0, fieldvar) '] .refval ∧ junkrefs(str, st1[r -- mkfs(class, ty0, fieldvar) '] .refval ' + acc, ty0, st1)
Proof step 51:
¬ r -- mkfs(class, ty0, fieldvar) ' ∈ st, ¬ r -- _type ∈ st, st1 .refs ∩ st .refs = ∅, st1[r -- mkfs(class, ty0, fieldvar) '] = refval(r0), st1[r -- _type] .type ≤ ty, is_obj(str, r, st1), mkfs(class, ty0, fieldvar) ' ∈ instfields(st1[r -- _type] .type .class), junkrefs(str, r0 ' + acc, ty0, st1 ∪ st), r ∈ st1, st1[r -- _type] .type ≤ ty, ∀ st1, st, r, str, ty. st1 .refs ∩ st .refs = ∅ ∧ r ∈ st1 ∧ junkrefs(str, r ' + acc, ty, st1 ∪ st) → junkrefs(str, r ' + acc, ty, st1) ⊦ r = jvmref, ∃ fs0. fs0 ' ∈ instfields(st1[r -- _type] .type .class) ∧ is_referencevalue(st1[r -- fs0 ']) ∧ r0 = st1[r -- fs0 '] .refval ∧ junkrefs(str, st1[r -- fs0 '] .refval ' + acc, fs0 .type, st1), mkfs(class, ty0, fieldvar) ' ∈ instfields(st1[r -- _type] .type .class) ∧ is_referencevalue(st1[r -- mkfs(class, ty0, fieldvar) ']) ∧ r0 = st1[r -- mkfs(class, ty0, fieldvar) '] .refval ∧ junkrefs(str, st1[r -- mkfs(class, ty0, fieldvar) '] .refval ' + acc, ty0, st1)

Rule argument

[speclemmaarg: ,¬ rk ∈ st0 → (st ∪ st0)[rk] = st[rk] ,[rk, st0, st] → [r -- mkfs(class, ty0, fieldvar) ', st, st1] ,F ,storefunsx , ,union-at-left ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (r -- mkfs(class, ty0, fieldvar) ', st, st1)]]