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Proof step 46 from proof validrefnotnull-union-at-right (previous step)

is_fskey(sk), sk ∈ instfields(class), validref(str, r, mkclasstype(class), st0) ⊦ r = jvmref, st[r -- sk] = noval, r -- sk ∈ st0, st0[r -- _type] .type = mkclasstype(st0[r -- _type] .type .class) ∧ (∃ fs. fs ' ∈ instfields(st0[r -- _type] .type .class) ∧ (is_reftype(fs .type) ∨ fs .type = abstract_type) ∧ st0[r -- fs '] .refval ≠ jvmref ∧ (¬ is_referencevalue(st0[r -- fs ']) ∨ ¬ st0[r -- (fs ' ' + _type ')] .type ≤ fs .type ∨ ¬ validref(str, st0[r -- fs '] .refval, fs .type, st0)))

User applied rule cut formula

And obtained the following new goals

Proof step 40:
is_classtype(st0[r -- _type] .type), is_fskey(sk), sk ∈ instfields(class), validref(str, r, mkclasstype(class), st0) ⊦ r = jvmref, st[r -- sk] = noval, r -- sk ∈ st0, st0[r -- _type] .type = mkclasstype(st0[r -- _type] .type .class) ∧ (∃ fs. fs ' ∈ instfields(st0[r -- _type] .type .class) ∧ (is_reftype(fs .type) ∨ fs .type = abstract_type) ∧ st0[r -- fs '] .refval ≠ jvmref ∧ (¬ is_referencevalue(st0[r -- fs ']) ∨ ¬ st0[r -- (fs ' ' + _type ')] .type ≤ fs .type ∨ ¬ validref(str, st0[r -- fs '] .refval, fs .type, st0)))
Proof step 45:
is_fskey(sk), sk ∈ instfields(class), validref(str, r, mkclasstype(class), st0) ⊦ is_classtype(st0[r -- _type] .type), r = jvmref, st[r -- sk] = noval, r -- sk ∈ st0, st0[r -- _type] .type = mkclasstype(st0[r -- _type] .type .class) ∧ (∃ fs. fs ' ∈ instfields(st0[r -- _type] .type .class) ∧ (is_reftype(fs .type) ∨ fs .type = abstract_type) ∧ st0[r -- fs '] .refval ≠ jvmref ∧ (¬ is_referencevalue(st0[r -- fs ']) ∨ ¬ st0[r -- (fs ' ' + _type ')] .type ≤ fs .type ∨ ¬ validref(str, st0[r -- fs '] .refval, fs .type, st0)))

Rule argument

[fma-arg: is_classtype(st0[r -- _type] .type)]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRAFMAS : (is_classtype(st0[r -- _type] .type))]]