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Proof step 56 from proof validrefs-levelsubset-01 (previous step)

¬ (r ≠ jvmref ∧ (¬ is_valid_ref(str0, r, st) ∨ ¬ st[r -- _type] .type ≤ ty0)), level⊆(str, str0), validrefs(str0, r ' + refs0, ty0, st), validref(str, r, ty, st), ∀ str, str0, ty0, st, ty. level⊆(str, str0) ∧ validrefs(str0, refs0, ty0, st) ∧ validref(str, refs0 .first, ty, st) → validrefs(str, refs0, ty0, st) ⊦ validrefs(str, r ' + refs0, ty0, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
⊦ validrefs(str, jvmref ' + refs, ty, st) ↔ refs = []
Proof step 55:
level⊆(str, str0), validrefs(str0, r ' + refs0, ty0, st), validref(str, r, ty, st), is_valid_ref(str0, r, st), st[r -- _type] .type ≤ ty0, ∀ str, str0, ty0, st, ty. level⊆(str, str0) ∧ validrefs(str0, refs0, ty0, st) ∧ validref(str, refs0 .first, ty, st) → validrefs(str, refs0, ty0, st) ⊦ r = jvmref, validrefs(str, r ' + refs0, ty0, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPNAMEDSEQ : junkrefs, , validref-null, ⊦ validref(str, jvmref, ty, st)])]]