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Proof step 27 from proof compatarray-mode (previous step)

st[r -- _type] .type = mkarraytype(ty), st[r -- _length] = intval(i), 0 ≤ i, r -- _length ∈ st, is_arrayref(r, i, st), r ∈ st ⊦ r = jvmref, (∀ j. ¬ j < 0 ∧ ¬ i ≤ j → compat(str, st[r -- j '], ty, st[_mode, val])) ↔ (∀ j. 0 ≤ j ∧ j < i → compat(str, st[r -- j '], ty, st))

User applied rule case distinction

And obtained the following new goals

Proof step 18:
∀ j. ¬ j < 0 ∧ ¬ i ≤ j → compat(str, st[r -- j '], ty, st[_mode, val]), st[r -- _type] .type = mkarraytype(ty), st[r -- _length] = intval(i), 0 ≤ i, r -- _length ∈ st, is_arrayref(r, i, st), r ∈ st ⊦ ∀ j. 0 ≤ j ∧ j < i → compat(str, st[r -- j '], ty, st), r = jvmref
Proof step 26:
∀ j. 0 ≤ j ∧ j < i → compat(str, st[r -- j '], ty, st), st[r -- _type] .type = mkarraytype(ty), st[r -- _length] = intval(i), 0 ≤ i, r -- _length ∈ st, is_arrayref(r, i, st), r ∈ st ⊦ ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → compat(str, st[r -- j '], ty, st[_mode, val]), r = jvmref

Rule argument

[CASEDARG : pos: right 2, ()]

Additional information

[[CONCRETESIMPRULES : ()]]