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Proof step 43 from proof same-subclasses-class-forward (previous step)

st[r -- mkfs(class, ty, fieldvar) '] = refval(r0), is_obj(str0, r, st), has_classtype(st[r0 -- _type] .type), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), same-subclasses(st[r -- _type] .type .class, str, str0), is_obj(str, r, st), is_obj(r, st), st[r0 -- _type] .type ≤ ty, is_valid_ref(str0, r0, st), ∀ class0. contains(str0, mkclasstype(st[r -- _type] .type .class), mkclasstype(class0)) → same-subclasses(class0, str, str0) ⊦ contains(str0, mkclasstype(st[r -- _type] .type .class), st[r0 -- _type] .type), r = jvmref, r0 = jvmref, contains(str0, mkclasstype(st[r -- _type] .type .class), st[r0 -- _type] .type .jtelemtype), junkref(str0, r0, st), same-subclasses(st[r0 -- _type] .type .jtelemtype .class, str, str0) ∧ (contains(str0, st[r0 -- _type] .type .jtelemtype, mkclasstype(class0)) → same-subclasses(class0, str, str0))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ contains(str, ty, ty0) ↔ type∃(str, ty) ∧ is_reftype(ty) ∧ ( (∃ ty1. ty1 ≤ ty ∧ type∃(str, ty1) ∧ type∃(str, ty0) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty0 ≤ fs .type)) ∧ (is_arraytype(ty1) → ty0 ≤ ty1 .type)) ∨ (∃ ty1, ty2. ty1 ≤ ty ∧ type∃(str, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty2 ≤ fs .type)) ∧ (is_arraytype(ty1) → ty2 ≤ ty1 .type) ∧ contains(str, ty2, ty0)))
Proof step 42:
st[r -- mkfs(class, ty, fieldvar) '] = refval(r0), is_obj(str0, r, st), has_classtype(st[r0 -- _type] .type), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), same-subclasses(st[r -- _type] .type .class, str, str0), is_obj(str, r, st), is_obj(r, st), st[r0 -- _type] .type ≤ ty, is_valid_ref(str0, r0, st), ∀ class0. contains(str0, mkclasstype(st[r -- _type] .type .class), mkclasstype(class0)) → same-subclasses(class0, str, str0) ⊦ type∃(str0, mkclasstype(st[r -- _type] .type .class)) ∧ is_reftype(mkclasstype(st[r -- _type] .type .class)) ∧ ( (∃ ty1. ty1 ≤ mkclasstype(st[r -- _type] .type .class) ∧ type∃(str0, ty1) ∧ type∃(str0, st[r0 -- _type] .type) ∧ (is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ st[r0 -- _type] .type ≤ fs .type)) ∧ (is_arraytype(ty1) → st[r0 -- _type] .type ≤ ty1 .type)) ∨ (∃ ty1, ty2. ty1 ≤ mkclasstype(st[r -- _type] .type .class) ∧ type∃(str0, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty2 ≤ fs .type)) ∧ (is_arraytype(ty1) → ty2 ≤ ty1 .type) ∧ contains(str0, ty2, st[r0 -- _type] .type))), r = jvmref, r0 = jvmref, contains(str0, mkclasstype(st[r -- _type] .type .class), st[r0 -- _type] .type .jtelemtype), junkref(str0, r0, st), same-subclasses(st[r0 -- _type] .type .jtelemtype .class, str, str0) ∧ (contains(str0, st[r0 -- _type] .type .jtelemtype, mkclasstype(class0)) → same-subclasses(class0, str, str0))

Rule argument

[crewrite-arg: contains-type-rec , F , [ty0, ty, str] → [st[r0 -- _type] .type, mkclasstype(st[r -- _type] .type .class), str0] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r0 -- _type] .type, mkclasstype(st[r -- _type] .type .class), str0)]]