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Proof step 19 from proof unchNorec-validrefs (previous step)

refs0 = r1 + refs, st[r -- _type] = st0[r -- _type], r1 = st[r -- mkfs(class, ty0, fieldvar) '] .refval, is_obj(str, r, st0), is_obj(str, r, st), st0[r -- _type] .type ≤ ty, unchangedNorec(r, st, st0), mkfs(class, ty0, fieldvar) ' ∈ instfields(st0[r -- _type] .type .class), is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ']), validrefs(str, refs0, ty0, st), ∀ str, ty, st, st0. validrefs(str, refs0, ty, st) ∧ (∀ r. r ∈ refs0 → unchangedNorec(r, st, st0)) → validrefs(str, refs0, ty, st0), ∀ r0. r0 ∈ refs0 → unchangedNorec(r0, st, st0) ⊦ r = jvmref, refs0 = [], ∃ fs. fs ' ∈ instfields(st0[r -- _type] .type .class) ∧ is_referencevalue(st0[r -- fs ']) ∧ r1 = st0[r -- fs '] .refval ∧ validrefs(str, refs0, fs .type, st0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
st[r -- _type] = st0[r -- _type], is_obj(str, r, st0), is_obj(str, r, st), st0[r -- _type] .type ≤ ty, unchangedNorec(r, st, st0), mkfs(class, ty0, fieldvar) ' ∈ instfields(st0[r -- _type] .type .class), is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ']), validrefs(str, st[r -- mkfs(class, ty0, fieldvar) '] .refval ' + refs, ty0, st), ∀ str0, ty1, st1, st2. validrefs(str0, st[r -- mkfs(class, ty0, fieldvar) '] .refval ' + refs, ty1, st1) ∧ (∀ r0. r0 = st[r -- mkfs(class, ty0, fieldvar) '] .refval ∨ r0 ∈ refs → unchangedNorec(r0, st1, st2)) → validrefs(str0, st[r -- mkfs(class, ty0, fieldvar) '] .refval ' + refs, ty1, st2), ∀ r0. r0 = st[r -- mkfs(class, ty0, fieldvar) '] .refval ∨ r0 ∈ refs → unchangedNorec(r0, st, st0) ⊦ r = jvmref, ∃ fs. fs ' ∈ instfields(st0[r -- _type] .type .class) ∧ is_referencevalue(st0[r -- fs ']) ∧ st[r -- mkfs(class, ty0, fieldvar) '] .refval = st0[r -- fs '] .refval ∧ validrefs(str, st[r -- mkfs(class, ty0, fieldvar) '] .refval ' + refs, fs .type, st0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ r ∈ r0 ' + refs ↔ r ≠ r0 ∧ ¬ r ∈ refs], [CSIMPSEQ : ⊦ r ∈ r0 ' ↔ r = r0], [CSIMPSEQ : ⊦ r ∈ refs + refs0 ↔ ¬ ¬ (r ∈ refs ∨ r ∈ refs0)], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' + refs ≠ []], [CSIMPSEQ : ⊦ r + refs = r ' + refs])]]