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Proof step 48 from proof validrefs-put-badclassfield (previous step)

¬ (is_array(str, r, st[r0 -- fs ', val]) ∧ (st[r0 -- fs ', val][r -- _type]) .type ≤ ty), is_array(str, r, st), st[r0 -- _type] .type = mkclasstype(class), st[r -- _type] .type ≤ ty, validrefs(str, r ' + r1 ' + refs, ty, st[r0 -- fs ', val]), ∀ 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]), is_obj(str, r, st[r0 -- fs ', val]) ∨ is_array(str, r, st[r0 -- fs ', val]) ⊦ r = jvmref, fs ' = _type, validrefs(str, r ' + r1 ' + refs, ty, st), junkref(str, r, st), fs ' ∈ instfields(class), r ∈ (r1 ' + refs) .butlast, dups((r1 ' + refs) .butlast)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 47:
st[r0 -- _type] .type = mkclasstype(class), is_array(str, r, st), st[r -- _type] .type ≤ ty, validrefs(str, r ' + r1 ' + refs, ty, st[r0 -- fs ', val]), is_obj(str, r, st[r0 -- fs ', val]), ∀ 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]) ⊦ r = jvmref, fs ' = _type, validrefs(str, r ' + r1 ' + refs, ty, st), junkref(str, r, st), fs ' ∈ instfields(class), r ∈ (r1 ' + refs) .butlast, dups((r1 ' + refs) .butlast)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_obj(str, r, st) → ¬ is_array(str, r, st)], [CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]