[Imprint][Data Privacy Statement][E-Mail]



View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 21 from proof same-subclasses-array-forward (previous step)

st[r -- _type] .type = mkarraytype(ty), st[r -- i '] = refval(r0), has_classtype(ty), is_array(str, r, st), same-subclasses(ty .jtelemtype .class, str, str0), is_array(str0, r, st), i < st[r -- _length] .intval, has_classtype(st[r0 -- _type] .type), 0 ≤ i, 0 < st[r -- _length] .intval, ∀ class0. contains(str0, ty .jtelemtype, mkclasstype(class0)) → same-subclasses(class0, str, str0) ⊦ r = jvmref, r0 = jvmref, ty .jtelemtype = mkclasstype(`java.lang.Object' .class), contains(str0, mkarraytype(ty), st[r0 -- _type] .type), contains(str0, ty .jtelemtype, st[r0 -- _type] .type .jtelemtype), st[r0 -- _type] .type .jtelemtype ≤ ty .jtelemtype, same-subclasses(st[r0 -- _type] .type .jtelemtype .class, str, str0) ∧ (contains(str0, st[r0 -- _type] .type .jtelemtype, mkclasstype(class)) → same-subclasses(class, str, str0)), ∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ st[r -- i0 '] .refval ≠ jvmref ∧ (¬ st[st[r -- i0 '] .refval -- _type] .type ≤ ty ∨ junkref(str0, st[r -- i0 '] .refval, st))

User applied rule exists right

And closed the goal!

Rule argument

[EXRARG : pos: right 8, [extquanttermlist: (i)abort:F, discard:T, computed:T]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ ¬ ty .jtelemtype ≤ ty0 .jtelemtype ∧ ty0 .jtelemtype ≠ mkclasstype (`java.lang.Object' .class) → ¬ ty ≤ ty0])], [EXTRATERMS : (i)]]