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Proof step 22 from proof validrefs-all-same (previous step)

st[r -- _type] = typeval(mkclasstype(class0)), st0[r -- _type] = typeval(mkclasstype(class0)), class+∃(str, class0), r -- _type ∈ st, class0 ≤ class1, r -- _type ∈ st0, r ∈ st0, r ∈ st, sk ∈ instfields(class0), goodfieldandtype(r, sk, st), ∀ sk. sk ∈ instfields(class0) → goodfieldandtype(r, sk, st), ∀ r0. (r0 = r ∨ r0 ∈ refs0) ∧ r0 ≠ jvmref → st[r0 -- _type] = st0[r0 -- _type] ∧ (is_classtype(st[r0 -- _type] .type) → (∀ sk. sk ∈ instfields(st[r0 -- _type] .type .class) → st[r0 -- sk] = st0[r0 -- sk])) ∧ ( is_arraytype(st[r0 -- _type] .type) → st[r0 -- _length] = st0[r0 -- _length] ∧ (∀ i. ¬ i < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i → st[r0 -- i '] = st0[r0 -- i '])), ∀ str0, ty0, st1, st2. validrefs(str0, refs0, ty0, st1) ∧ (∀ r0. r0 ∈ refs0 ∧ r0 ≠ jvmref → st1[r0 -- _type] = st2[r0 -- _type] ∧ (is_classtype(st1[r0 -- _type] .type) → (∀ sk. sk ∈ instfields(st1[r0 -- _type] .type .class) → st1[r0 -- sk] = st2[r0 -- sk])) ∧ ( is_arraytype(st1[r0 -- _type] .type) → st1[r0 -- _length] = st2[r0 -- _length] ∧ (∀ i. 0 ≤ i ∧ i < st1[r0 -- _length] .intval → st1[r0 -- i '] = st2[r0 -- i ']))) → validrefs(str0, refs0, ty0, st2), refs0 = [] ∨ mkfs(class, ty1, fieldvar) ' ∈ instfields(class0) ∧ is_referencevalue(st[r -- mkfs(class, ty1, fieldvar) ']) ∧ refs0 .first = st[r -- mkfs(class, ty1, fieldvar) '] .refval ∧ validrefs(str, refs0, ty1, st), ∀ sk. sk ∈ instfields(class0) → st[r -- sk] = st0[r -- sk] ⊦ r = jvmref, is_fskey(sk) ∧ r -- sk ∈ st0 ∧ okval(st0[r -- sk], sk .fs .type), is_abstract(class0), validrefs(str, r ' + refs0, mkclasstype(class1), st0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
st[r -- _type] = typeval(mkclasstype(class0)), st0[r -- _type] = typeval(mkclasstype(class0)), is_fskey(sk), class+∃(str, class0), r -- _type ∈ st, class0 ≤ class1, r -- _type ∈ st0, r ∈ st0, r ∈ st, sk ∈ instfields(class0), r -- sk ∈ st, okval(st[r -- sk], sk .fs .type), ∀ sk. sk ∈ instfields(class0) → goodfieldandtype(r, sk, st), ∀ r0. (r0 = r ∨ r0 ∈ refs0) ∧ r0 ≠ jvmref → st[r0 -- _type] = st0[r0 -- _type] ∧ (is_classtype(st[r0 -- _type] .type) → (∀ sk. sk ∈ instfields(st[r0 -- _type] .type .class) → st[r0 -- sk] = st0[r0 -- sk])) ∧ ( is_arraytype(st[r0 -- _type] .type) → st[r0 -- _length] = st0[r0 -- _length] ∧ (∀ i. ¬ i < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i → st[r0 -- i '] = st0[r0 -- i '])), ∀ str0, ty0, st1, st2. validrefs(str0, refs0, ty0, st1) ∧ (∀ r0. r0 ∈ refs0 ∧ r0 ≠ jvmref → st1[r0 -- _type] = st2[r0 -- _type] ∧ (is_classtype(st1[r0 -- _type] .type) → (∀ sk. sk ∈ instfields(st1[r0 -- _type] .type .class) → st1[r0 -- sk] = st2[r0 -- sk])) ∧ ( is_arraytype(st1[r0 -- _type] .type) → st1[r0 -- _length] = st2[r0 -- _length] ∧ (∀ i. 0 ≤ i ∧ i < st1[r0 -- _length] .intval → st1[r0 -- i '] = st2[r0 -- i ']))) → validrefs(str0, refs0, ty0, st2), refs0 = [] ∨ mkfs(class, ty1, fieldvar) ' ∈ instfields(class0) ∧ is_referencevalue(st[r -- mkfs(class, ty1, fieldvar) ']) ∧ refs0 .first = st[r -- mkfs(class, ty1, fieldvar) '] .refval ∧ validrefs(str, refs0, ty1, st), ∀ sk. sk ∈ instfields(class0) → st[r -- sk] = st0[r -- sk] ⊦ r = jvmref, is_abstract(class0), validrefs(str, r ' + refs0, mkclasstype(class1), st0), okval(st0[r -- sk], sk .fs .type) ∧ r -- sk ∈ st0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_fskey(sk) → ( goodfieldandtype(r, sk, st) ↔ r -- sk ∈ st ∧ okval (st[r -- sk], sk .fs .type))], [CSIMPSEQ : ⊦ ¬ is_indexkey(sk) ↔ is_fskey(sk)], [CSIMPSEQ : ⊦ is_indexkey(sk) → ¬ goodfieldandtype(r, sk, st)], [CSIMPSEQ : ⊦ ¬ is_fskey(sk) ↔ is_indexkey(sk)])]]