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Proof step 98 from proof validrefs-subset-equiv (previous step)

¬ (r ≠ jvmref ∧ ¬ is_valid_ref(str, r, st)), validrefs(str, r ' + refs, ty, st0), st ⊆ st0, ∀ st, st0, ty, r, str, refs0. # refs0 < # refs → (validrefs(str, r ' + refs0, ty, st0) ∧ st ⊆ st0 ∧ validref(str, r, st[r -- _type] .type, st) → validrefs(str, r ' + refs0, ty, st)) ⊦ junkref(str, r, st), validrefs(str, r ' + refs, ty, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
⊦ validrefs(str, jvmref ' + refs, ty, st) ↔ refs = []
Proof step 97:
validrefs(str, r ' + refs, ty, st0), st ⊆ st0, is_valid_ref(str, r, st), ∀ st, st0, ty, r, str, refs0. # refs0 < # refs → (validrefs(str, r ' + refs0, ty, st0) ∧ st ⊆ st0 ∧ validref(str, r, st[r -- _type] .type, st) → validrefs(str, r ' + refs0, ty, st)) ⊦ r = jvmref, junkref(str, r, st), validrefs(str, r ' + refs, ty, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]