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Proof step 43 from proof at-put-prim (previous step)

is_referencevalue(st[r0 -- (sk0 ' + sks0)]), fits(r0, sk0 ' + sks0, st), ∀ st, r0, r, sk, val, str. is_referencevalue(st[r0 -- sks0]) ∧ fits(r0, sks0, st) → sks0 = [] ∨ (st[r -- sk, val][r0 -- sks0]) = st[r0 -- sks0] ∨ is_referencevalue(st[r -- sk]) ∨ junkref(str, r, st) ∨ junkref(str, r0, st) ⊦ (st[r -- sk, val][r0 -- (sk0 ' + sks0)]) = st[r0 -- (sk0 ' + sks0)], is_referencevalue(st[r -- sk]), junkref(str, r, st), junkref(str, r0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ fits(r, sk ' + sks, st) ↔ r ≠ jvmref ∧ is_referencevalue(st[r -- sk]) ∧ (is_classtype(st[r -- _type] .type) → sk ∈ instfields(st[r -- _type] .type .class)) ∧ (is_arraytype(st[r -- _type] .type) → is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r -- _length] .intval) ∧ fits(st[r -- sk] .refval, sks, st)
Proof step 42:
is_referencevalue(st[r0 -- (sk0 ' + sks0)]), r0 ≠ jvmref ∧ is_referencevalue(st[r0 -- sk0]) ∧ (is_classtype(st[r0 -- _type] .type) → sk0 ∈ instfields(st[r0 -- _type] .type .class)) ∧ (is_arraytype(st[r0 -- _type] .type) → is_indexkey(sk0) ∧ 0 ≤ sk0 .index ∧ sk0 .index < st[r0 -- _length] .intval) ∧ fits(st[r0 -- sk0] .refval, sks0, st), ∀ st, r0, r, sk, val, str. is_referencevalue(st[r0 -- sks0]) ∧ fits(r0, sks0, st) → sks0 = [] ∨ (st[r -- sk, val][r0 -- sks0]) = st[r0 -- sks0] ∨ is_referencevalue(st[r -- sk]) ∨ junkref(str, r, st) ∨ junkref(str, r0, st) ⊦ (st[r -- sk, val][r0 -- (sk0 ' + sks0)]) = st[r0 -- (sk0 ' + sks0)], is_referencevalue(st[r -- sk]), junkref(str, r, st), junkref(str, r0, st)

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: fits-storekeys-rec antecedent: succedent: fits(r, sk ' + sks, st) ↔ r ≠ jvmref ∧ is_referencevalue(st[r -- sk]) ∧ ( is_classtype(st[r -- _type] .type) → sk ∈ instfields(st[r -- _type] .type .class)) ∧ ( is_arraytype(st[r -- _type] .type) → is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r -- _length] .intval) ∧ fits(st[r -- sk] .refval, sks, st) substlist: [st, sks, sk, r] → [st, sks0, sk0, r0] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 1)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, sks0, sk0, r0)]]