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Proof step 52 from proof disjoint-nojunk-newref-subset-01 (previous step)

refs1 = [], (r1 ' + refs0) .last = (r ' + refs1) .last, r1 ∈ st, st ⊆ st1, newref(r, st), validrefs(str, r ' + refs1, st1[r -- _type] .type, st1), validrefs(str, r1 ' + refs0, st[r1 -- _type] .type, st1), r1 -- _type ∈ st ⊦ r = r1, r = jvmref, (r ' + refs1) .last = jvmref, path∃(str, r, (r ' + refs1) .last, st1), junkref(str, r1, st), ¬ path∃(str, r, refs1 .last, st1) ∧ (r ' + refs1) .last ∈ refs1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 51:
validrefs(str, (r1 ' + refs0) .last ', st1[(r1 ' + refs0) .last -- _type] .type, st1), newref((r1 ' + refs0) .last, st), st ⊆ st1, r1 ∈ st, r1 -- _type ∈ st, validrefs(str, r1 ' + refs0, st[r1 -- _type] .type, st1) ⊦ (r1 ' + refs0) .last = jvmref, (r1 ' + refs0) .last = r1, is_valid_ref(str, (r1 ' + refs0) .last, st1), junkref(str, r1, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ newref(r, st) → r ≠ jvmref], [CSIMPSEQ : ⊦ ¬ r ∈ []], [CSIMPSEQ : ⊦ path∃(str, r, r, st) ↔ r = jvmref ∨ r ≠ jvmref ∧ is_valid_ref(str, r, st)], [CSIMPSEQ : ⊦ r ' .last = r], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ refs + [] = refs])]]