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Proof step 126 from proof unchanged-junkrefs-level (previous step)

is_valid_ref(str0, r, st) ↔ is_valid_ref(str0, r, st1), st1[r -- _type] .type ≤ ty, is_valid_ref(str, r, st1), junkrefs(str, r ' + refs0, ty, st), unchanged(str0, r, st, st1), level⊆(str, str0), ∀ str0, st, st1, str, ty. unchanged(str0, refs0 .first, st, st1) ∧ junkrefs(str, refs0, ty, st) ∧ level⊆(str, str0) → junkrefs(str, refs0, ty, st1), ∀ r0. (path∃(str0, r, r0, st) ↔ path∃(str0, r, r0, st1)) ∧ (path∃(str0, r, r0, st) → unchangedNorec(r0, st, st1)), is_valid_ref(str0, r, st1) → unchangedNorec(r, st, st1) ⊦ is_valid_ref(str0, r, st1), r = jvmref, junkrefs(str, r ' + refs0, ty, st1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 125:
st1[r -- _type] .type ≤ ty, is_valid_ref(str, r, st1), junkrefs(str, r ' + refs0, ty, st), unchanged(str0, r, st, st1), level⊆(str, str0), ∀ str0, st, st1, str, ty. unchanged(str0, refs0 .first, st, st1) ∧ junkrefs(str, refs0, ty, st) ∧ level⊆(str, str0) → junkrefs(str, refs0, ty, st1) ⊦ r = jvmref, is_valid_ref(str0, r, st1), junkrefs(str, r ' + refs0, ty, st1), is_valid_ref(str0, r, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : cyclic, , pathex-not-is-validref-02, ⊦ ¬ is_valid_ref(str, r, st) ∧ r ≠ jvmref → ¬ path∃(str, r, r1, st)], [CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]