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Proof step 33 from proof validrefs-all-same (previous step)

st[r -- _type] = st0[r -- _type], st0[r -- _type] .type = mkclasstype(class0), is_obj(str, r, st), class0 ≤ class1, ∀ 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, class+∃(str, st0[r -- _type] .type .class) ∧ ¬ is_abstract(st0[r -- _type] .type .class) ∧ r ≠ jvmref ∧ r -- _type ∈ st0 ∧ is_typevalue(st0[r -- _type]) ∧ is_classtype(st0[r -- _type] .type) ∧ (r -- _type) × st0[r -- _type] ∈ st0 ∧ goodfieldsandtypes(r, instfields(st0[r -- _type] .type .class), st0), validrefs(str, r ' + refs0, mkclasstype(class1), st0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
st0[r -- _type] .type = mkclasstype(class0), st[r -- _type] = st0[r -- _type], r ∈ st0, r -- _type ∈ st0, is_typevalue(st0[r -- _type]), class0 ≤ class1, is_obj(str, r, st), ∀ sk. sk ∈ instfields(class0) → st[r -- sk] = st0[r -- sk], 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), ∀ 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), ∀ 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 '])) ⊦ r = jvmref, validrefs(str, r ' + refs0, mkclasstype(class1), st0), class+∃(str, class0) ∧ ¬ is_abstract(class0) ∧ goodfieldsandtypes(r, instfields(class0), st0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_classtype(mkclasstype(class))], [CSIMPSEQ : ⊦ mkclasstype(class) .class = class], [CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ ¬ is_typevalue(noval)], [CSIMPSEQ : ⊦ ∅[rk] = noval], [CSIMPSEQ : ⊦ ¬ rk ∈ st → st[rk] = ∅[rk]], [CSIMPSEQ : ⊦ mkclasstype(class) ≠ void_type], [CSIMPSEQ : ⊦ ¬ is_typevalue(val) → val .type = void_type], [CSIMPSEQ : ⊦ rk × val ∈ st ↔ rk ∈ st ∧ st[rk] = val])]]