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Proof step 56 from proof fits-put-short-02 (previous step)

is_shortvalue(st[r1 -- fs ']), fits(r, sk ' + sks0, st), ∀ r, st, r1, fs, str, sho. fits(r, sks0, st) ∧ is_shortvalue(st[r1 -- fs ']) → junkref(str, r, st) ∨ fits(r, sks0, st[r1 -- fs ', shortval(sho)]) ⊦ junkref(str, r, st), r ≠ jvmref ∧ is_referencevalue(st[r1 -- fs ', shortval(sho)][r -- sk]) ∧ (is_classtype((st[r1 -- fs ', shortval(sho)][r -- _type]) .type) → sk ∈ instfields((st[r1 -- fs ', shortval(sho)][r -- _type]) .type .class)) ∧ ( is_arraytype((st[r1 -- fs ', shortval(sho)][r -- _type]) .type) → is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < (st[r1 -- fs ', shortval(sho)][r -- _length]) .intval) ∧ fits((st[r1 -- fs ', shortval(sho)][r -- sk]) .refval, sks0, st[r1 -- fs ', shortval(sho)])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
⊦ fits(jvmref, sks, st) ↔ sks = []
Proof step 55:
is_shortvalue(st[r1 -- fs ']), fits(r, sk ' + sks0, st), ∀ r, st, r1, fs, str, sho. fits(r, sks0, st) ∧ is_shortvalue(st[r1 -- fs ']) → junkref(str, r, st) ∨ fits(r, sks0, st[r1 -- fs ', shortval(sho)]) ⊦ r = jvmref, junkref(str, r, st), fits((st[r1 -- fs ', shortval(sho)][r -- sk]) .refval, sks0, st[r1 -- fs ', shortval(sho)]) ∧ ( is_arraytype((st[r1 -- fs ', shortval(sho)][r -- _type]) .type) → ¬ is_fskey(sk) ∧ ¬ sk .index < 0 ∧ ¬ (st[r1 -- fs ', shortval(sho)][r -- _length]) .intval ≤ sk .index) ∧ (is_classtype((st[r1 -- fs ', shortval(sho)][r -- _type]) .type) → sk ∈ instfields((st[r1 -- fs ', shortval(sho)][r -- _type]) .type .class)) ∧ is_referencevalue(st[r1 -- fs ', shortval(sho)][r -- sk])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPSEQ : ⊦ sk ' ≠ []], [CSIMPSEQ : ⊦ ¬ sks + sks0 ≠ [] ↔ sks = [] ∧ sks0 = []], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ ¬ is_indexkey(sk) ↔ is_fskey(sk)])]]