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Proof step 45 from proof validrefnotnull-union-at-right (previous step)

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)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 41:
⊦ validref(str, r, ty, st) ↔ r = jvmref ∨ st[r -- _type] .type ≤ ty ∧ ¬ junkref(str, r, st)
Proof step 44:
is_fskey(sk), sk ∈ instfields(class), r = jvmref ∨ st0[r -- _type] .type ≤ mkclasstype(class) ∧ ¬ junkref(str, r, 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

[crewrite-arg: validref-def , F , [st, ty, r, str] → [st0, mkclasstype(class), r, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st0, mkclasstype(class), r, str)]]