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Proof step 202 from proof pathex-put-nopathex (previous step)

validrefs(str, r ' + refs0, st[r -- _type] .type, st), is_obj(str, r, st) ∨ is_array(str, r, st), ∀ val, r0, sk, st, r, str, refs. # refs < # refs0 → ( validrefs(str, r ' + refs, st[r -- _type] .type, st) → sk = _type ∨ path∃(str, r, r0, st) ∨ junkref(str, r, st) ∨ path∃(str, r, (r ' + refs) .last, st[r0 -- sk, val])) ⊦ sk = _type, r = jvmref, path∃(str, r, (r ' + refs0) .last, st[r0 -- sk, val]), junkref(str, r, st), path∃(str, r, r0, st)

User applied rule case distinction

And obtained the following new goals

Proof step 145:
is_obj(str, r, st), validrefs(str, r ' + refs0, st[r -- _type] .type, st), ∀ val, r0, sk, st, r, str, refs. # refs < # refs0 → ( validrefs(str, r ' + refs, st[r -- _type] .type, st) → sk = _type ∨ path∃(str, r, r0, st) ∨ junkref(str, r, st) ∨ path∃(str, r, (r ' + refs) .last, st[r0 -- sk, val])) ⊦ sk = _type, r = jvmref, path∃(str, r, (r ' + refs0) .last, st[r0 -- sk, val]), junkref(str, r, st), path∃(str, r, r0, st)
Proof step 201:
is_array(str, r, st), validrefs(str, r ' + refs0, st[r -- _type] .type, st), ∀ val, r0, sk, st, r, str, refs. # refs < # refs0 → ( validrefs(str, r ' + refs, st[r -- _type] .type, st) → sk = _type ∨ path∃(str, r, r0, st) ∨ junkref(str, r, st) ∨ path∃(str, r, (r ' + refs) .last, st[r0 -- sk, val])) ⊦ sk = _type, r = jvmref, path∃(str, r, (r ' + refs0) .last, st[r0 -- sk, val]), junkref(str, r, st), path∃(str, r, r0, st)

Rule argument

[CASEDARG : pos: left 2, ()]

Additional information

[[CONCRETESIMPRULES : ()]]