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Proof step 13 from proof validrefs-all-same (previous step)

st0[r -- _type] = typeval(mkclasstype(class0)), st[r -- _type] = typeval(mkclasstype(class0)), st[r -- mkfs(class2, ty, fieldvar0) '] = noval, r -- mkfs(class2, ty, fieldvar0) ' ∈ st, mkfs(class2, ty, fieldvar0) ' ∈ instfields(class0), r ∈ st, r ∈ st0, r -- _type ∈ st0, class0 ≤ class1, r -- _type ∈ st, class+∃(str, class0), okval(noval, ty), ∀ sk. sk ∈ instfields(class0) → goodfieldandtype(r, sk, 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), is_abstract(class0), r -- mkfs(class2, ty, fieldvar0) ' ∈ st0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ okval(val, ty) ↔ is_boolvalue(val) ∧ ty = boolean_type ∨ is_integervalue(val) ∧ ty = int_type ∨ is_shortvalue(val) ∧ ty = short_type ∨ is_bytevalue(val) ∧ ty = byte_type ∨ is_longvalue(val) ∧ ty = long_type ∨ is_floatvalue(val) ∧ ty = float_type ∨ is_doublevalue(val) ∧ ty = double_type ∨ is_charvalue(val) ∧ ty = char_type ∨ is_referencevalue(val) ∧ (is_classtype(ty) ∨ is_arraytype(ty) ∨ ty = void_type)

Rule argument

[x0lemmaarg: spec-name: valuefuns instance-name: lemma-name: okval-case antecedent: succedent: okval(val, ty) ↔ is_boolvalue(val) ∧ ty = boolean_type ∨ is_integervalue(val) ∧ ty = int_type ∨ is_shortvalue(val) ∧ ty = short_type ∨ is_bytevalue(val) ∧ ty = byte_type ∨ is_longvalue(val) ∧ ty = long_type ∨ is_floatvalue(val) ∧ ty = float_type ∨ is_doublevalue(val) ∧ ty = double_type ∨ is_charvalue(val) ∧ ty = char_type ∨ is_referencevalue(val) ∧ ( is_classtype(ty) ∨ is_arraytype(ty) ∨ ty = void_type) substlist: [ty, val] → [ty, noval] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 11)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_boolvalue(noval)], [CSIMPSEQ : ⊦ ¬ is_integervalue(noval)], [CSIMPSEQ : ⊦ ¬ is_shortvalue(noval)], [CSIMPSEQ : ⊦ ¬ is_bytevalue(noval)], [CSIMPSEQ : ⊦ ¬ is_longvalue(noval)], [CSIMPSEQ : ⊦ ¬ is_floatvalue(noval)], [CSIMPSEQ : ⊦ ¬ is_doublevalue(noval)], [CSIMPSEQ : ⊦ ¬ is_charvalue(noval)], [CSIMPSEQ : ⊦ ¬ is_referencevalue(noval)])], [EXTRATERMS : (ty, noval)]]