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Proof step 8 from proof validref-put-any-01 (conclusion)

⊦ validref(str, r, ty, st) ∧ ( is_fskey(rk .key) → (is_referencevalue(val) → validref(str, val .refval, rk .key .fs .type, st) ∧ is_reftype(rk .key .fs .type)) ∧ (¬ is_referencevalue(val) → okval(val, rk .key .fs .type) ∧ rk .key .fs .type ≠ void_type ∧ rk .key ≠ _length)) ∧ ( is_indexkey(rk .key) → ( is_referencevalue(val) → validref(str, val .refval, st[rk .ref -- _type] .type .type, st) ∧ rk .ref ≠ jvmref ∧ is_arraytype(st[rk .ref -- _type] .type) ∧ (val .refval = jvmref → is_reftype(st[rk .ref -- _type] .type .type))) ∧ (¬ is_referencevalue(val) → okval(val, st[rk .ref -- _type] .type .type))) → validref(str, r, ty, st[rk, val])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
validref(str, r, ty, st), ¬ is_indexkey(rk .key) → (is_referencevalue(val) → validref(str, val .refval, rk .key .fs .type, st) ∧ is_reftype(rk .key .fs .type)) ∧ (¬ is_referencevalue(val) → okval(val, rk .key .fs .type) ∧ rk .key .fs .type ≠ void_type ∧ rk .key ≠ _length), ¬ is_fskey(rk .key) → ( is_referencevalue(val) → validref(str, val .refval, st[rk .ref -- _type] .type .type, st) ∧ rk .ref ≠ jvmref ∧ is_arraytype(st[rk .ref -- _type] .type) ∧ (val .refval = jvmref → is_reftype(st[rk .ref -- _type] .type .type))) ∧ (¬ is_referencevalue(val) → okval(val, st[rk .ref -- _type] .type .type)) ⊦ validref(str, r, ty, st[rk, val])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_indexkey(sk) ↔ is_fskey(sk)], [CSIMPSEQ : ⊦ ¬ is_fskey(sk) ↔ is_indexkey(sk)])]]