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Proof step 58 from proof unchNorec-validrefs (previous step)

validrefs(str, r ' + refs0, ty, st), is_obj(str, r, st) ∨ is_array(str, r, st), st[r -- _type] .type ≤ ty, ∀ str, ty, st, st0. validrefs(str, refs0, ty, st) ∧ (∀ r. r ∈ refs0 → unchangedNorec(r, st, st0)) → validrefs(str, refs0, ty, st0), ∀ r0. r0 = r ∨ r0 ∈ refs0 → unchangedNorec(r0, st, st0) ⊦ r = jvmref, validrefs(str, r ' + refs0, ty, st0)

User applied rule case distinction

And obtained the following new goals

Proof step 30:
is_obj(str, r, st), validrefs(str, r ' + refs0, ty, st), st[r -- _type] .type ≤ ty, ∀ str, ty, st, st0. validrefs(str, refs0, ty, st) ∧ (∀ r. r ∈ refs0 → unchangedNorec(r, st, st0)) → validrefs(str, refs0, ty, st0), ∀ r0. r0 = r ∨ r0 ∈ refs0 → unchangedNorec(r0, st, st0) ⊦ r = jvmref, validrefs(str, r ' + refs0, ty, st0)
Proof step 57:
is_array(str, r, st), validrefs(str, r ' + refs0, ty, st), st[r -- _type] .type ≤ ty, ∀ str, ty, st, st0. validrefs(str, refs0, ty, st) ∧ (∀ r. r ∈ refs0 → unchangedNorec(r, st, st0)) → validrefs(str, refs0, ty, st0), ∀ r0. r0 = r ∨ r0 ∈ refs0 → unchangedNorec(r0, st, st0) ⊦ r = jvmref, validrefs(str, r ' + refs0, ty, st0)

Rule argument

[CASEDARG : pos: left 2, ()]

Additional information

[[CONCRETESIMPRULES : ()]]