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Proof step 9 from proof is_valid_ref-levelsubset (previous step)

level⊆(str, str0), class+∃(str, st[r -- _type] .type .class) ∧ ¬ is_abstract(st[r -- _type] .type .class) ∧ is_obj(r, st) ∨ type∃(str, st[r -- _type] .type) ∧ st[r -- _type] .type .jtelemtype ≠ void_type ∧ st[r -- _type] .type .jtelemtype ≠ abstract_type ∧ is_array(r, st) ⊦ type∃(str0, st[r -- _type] .type) ∧ st[r -- _type] .type .jtelemtype ≠ void_type ∧ st[r -- _type] .type .jtelemtype ≠ abstract_type ∧ is_array(r, st), class+∃(str0, st[r -- _type] .type .class) ∧ ¬ is_abstract(st[r -- _type] .type .class) ∧ is_obj(r, st)

User applied rule case distinction

And obtained the following new goals

Proof step 7:
⊦ class+∃(str, class) ∧ level⊆(str, str0) → (¬ class+∃(str0, class) ↔ false)
Proof step 8:
⊦ type∃(str, ty) ∧ ¬ type∃(str0, ty) → ¬ level⊆(str, str0)

Rule argument

[CASEDARG : pos: left 2, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : addfuns, , isobj-type-08, ⊦ is_obj(r, st) → st[r -- _type] .type .jtelemtype = st[r -- _type] .type], [CSIMPNAMEDSEQ : addfuns, , isobj-isarray, ⊦ is_obj(r, st) → ¬ is_array(r, st)])]]