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Proof step 44 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) ⊦ 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 cut formula

And obtained the following new goals

Proof step 22:
contains(str0, mkclasstype(st[r -- _type] .type .class), st[r0 -- _type] .type), 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) ⊦ 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))
Proof step 43:
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))

Rule argument

[fma-arg: contains (str0, mkclasstype(st[r -- _type] .type .class), st[r0 -- _type] .type) ]

Additional information

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