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Proof step 75 from proof validrefs-put-badclassfield (previous step)

is_classtype(st[r0 -- _type] .type), validrefs(str, r ' + r1 ' + refs, ty, st[r0 -- fs ', val]), is_obj(str, r, st[r0 -- fs ', val]) ∨ is_array(str, r, st[r0 -- fs ', val]), st[r -- _type] .type ≤ ty, ∀ str0, ty0, st0, fs0, r2, val0. ¬ validrefs(str0, r1 ' + refs, ty0, st0) ∧ ¬ junkref(str0, r1, st0) ∧ fs0 ' ≠ _type ∧ is_classtype(st0[r2 -- _type] .type) ∧ ¬ fs0 ' ∈ instfields(st0[r2 -- _type] .type .class) → ¬ validrefs(str0, r1 ' + refs, ty0, st0[r2 -- fs0 ', val0]) ⊦ fs ' = _type, r = jvmref, dups((r1 ' + refs) .butlast), r ∈ (r1 ' + refs) .butlast, fs ' ∈ instfields(st[r0 -- _type] .type .class), junkref(str, r, st), validrefs(str, r ' + r1 ' + refs, ty, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 74:
st[r0 -- _type] .type = mkclasstype(class), is_classtype(st[r0 -- _type] .type), validrefs(str, r ' + r1 ' + refs, ty, st[r0 -- fs ', val]), is_obj(str, r, st[r0 -- fs ', val]) ∨ is_array(str, r, st[r0 -- fs ', val]), st[r -- _type] .type ≤ ty, ∀ str0, ty0, st0, fs0, r2, val0. ¬ validrefs(str0, r1 ' + refs, ty0, st0) ∧ ¬ junkref(str0, r1, st0) ∧ fs0 ' ≠ _type ∧ is_classtype(st0[r2 -- _type] .type) ∧ ¬ fs0 ' ∈ instfields(st0[r2 -- _type] .type .class) → ¬ validrefs(str0, r1 ' + refs, ty0, st0[r2 -- fs0 ', val0]) ⊦ fs ' = _type, r = jvmref, dups((r1 ' + refs) .butlast), r ∈ (r1 ' + refs) .butlast, fs ' ∈ instfields(class), junkref(str, r, st), validrefs(str, r ' + r1 ' + refs, ty, st)

Rule argument

[speclemmaarg: ,is_classtype(ty) → (class = ty .class ↔ ty = mkclasstype(class)) ,[ty, class] → [st[r0 -- _type] .type, class] ,T ,javatype , ,elim-02 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_classtype(ty) → ( class = ty .class ↔ ty = mkclasstype(class))])], [EXTRATERMS : (st[r0 -- _type] .type, class)]]