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Proof step 44 from proof put-switch-primval-field-field (previous step)

st[r -- sks1] = refval(r1), fits(r, sks1 + mkfs(class, ty, fieldvar) ' ', st), fits(r0, sks + mkfs(class0, ty0, fieldvar0) ' ', st), refval(r1) ≠ st[r0 -- sks] ∨ class ≠ class0 ∨ ty ≠ ty0 ∨ fieldvar ≠ fieldvar0 ⊦ (st[r1 -- mkfs(class, ty, fieldvar) ', val][(st[r1 -- mkfs(class, ty, fieldvar) ', val][r0 -- sks]) .refval -- mkfs(class0, ty0, fieldvar0) ', val0] ) = (st[st[r0 -- sks] .refval -- mkfs(class0, ty0, fieldvar0) ', val0][r -- (sks1 + mkfs(class, ty, fieldvar) ' '), val]), junkref(str, r0, st), junkref(str, r, st), is_reftype(ty0), is_reftype(ty), is_referencevalue(val0), is_referencevalue(val)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ st[r -- (sks + sk '), val] = st[st[r -- sks] .refval -- sk, val]
Proof step 43:
st[r -- sks1] = refval(r1), fits(r, sks1 + mkfs(class, ty, fieldvar) ' ', st), fits(r0, sks + mkfs(class0, ty0, fieldvar0) ' ', st), refval(r1) ≠ st[r0 -- sks] ∨ class ≠ class0 ∨ ty ≠ ty0 ∨ fieldvar ≠ fieldvar0 ⊦ (st[r1 -- mkfs(class, ty, fieldvar) ', val][(st[r1 -- mkfs(class, ty, fieldvar) ', val][r0 -- sks]) .refval -- mkfs(class0, ty0, fieldvar0) ', val0] ) = (st[st[r0 -- sks] .refval -- mkfs(class0, ty0, fieldvar0) ', val0] [(st[st[r0 -- sks] .refval -- mkfs(class0, ty0, fieldvar0) ', val0][r -- sks1]) .refval -- mkfs(class, ty, fieldvar) ', val ] ), junkref(str, r0, st), junkref(str, r, st), is_reftype(ty0), is_reftype(ty), is_referencevalue(val0), is_referencevalue(val)

Rule argument

[x0lemmaarg: spec-name: storefuns instance-name: lemma-name: put-last-rec-better antecedent: succedent: st[r -- (sks + sk '), val] = st[st[r -- sks] .refval -- sk, val] substlist: [val, sk, sks, r, st] → [val, mkfs(class, ty, fieldvar) ', sks1, r, st[ st[r0 -- sks] .refval -- mkfs(class0, ty0, fieldvar0) ', val0]] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 0, 1, 1)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (val, mkfs(class, ty, fieldvar) ', sks1, r, st[ st[r0 -- sks] .refval -- mkfs(class0, ty0, fieldvar0) ', val0])]]