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Proof step 58 from proof getbytearray-pseq-02 (previous step)

validref(`docs2store', r, mkarraytype(byte_type), st), ps=(r, st, r1, st1), i < st[r -- _length] .intval, i + i1 ≤ st[r -- _length] .intval, 0 ≤ i, 0 < st[r -- _length] .intval, 0 ≤ i1 ⊦ getbytearray(r, i, i1, st) = getbytearray(r1, i, i1, st1), r = jvmref

User applied rule induction

And obtained the following new goals

Proof step 57:
validref(`docs2store', r, mkarraytype(byte_type), st) ∧ ps=(r, st, r1, st1) ∧ i < st[r -- _length] .intval ∧ i + i1 ≤ st[r -- _length] .intval ∧ 0 ≤ i ∧ 0 < st[r -- _length] .intval ∧ 0 ≤ i1, ∀ i1, st1, r1, i0, r0, st0. i→n(st0[r0 -- _length] .intval - i0) < i→n(st[r -- _length] .intval - i) → ( validref(`docs2store', r0, mkarraytype(byte_type), st0) ∧ ps=(r0, st0, r1, st1) ∧ i0 < st0[r0 -- _length] .intval ∧ i0 + i1 ≤ st0[r0 -- _length] .intval ∧ 0 ≤ i0 ∧ 0 < st0[r0 -- _length] .intval ∧ 0 ≤ i1 → getbytearray(r0, i0, i1, st0) = getbytearray(r1, i0, i1, st1) ∨ r0 = jvmref) ⊦ getbytearray(r, i, i1, st) = getbytearray(r1, i, i1, st1) ∨ r = jvmref

Rule argument

[INDHYPARG : [STANDARDINDUCTIONTYPE : ], true, false, i→n(st[r -- _length] .intval - i), [] → [], <]

Additional information

[[CONCRETESIMPRULES : ([CSIMPLESSPRED : <])], [EXTRATERMS : (i→n(st[r -- _length] .intval - i))]]