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Proof step 76 from proof onlymod-is-update (previous step)

r0 -- sk ∈ st1, r0 -- sk ∈ st0, onlyModified(r, st0, st1), r0 ∈ st1, r0 ∈ st0, ∀ st, r1, st2. ¬ # st0 ≤ # st2 → (onlyModified(r1, st2, st) → (∃ fis. st = update(r1, fis, st2) ∧ validFields(r1, fis, st2))) ⊦ st0[r0 -- sk] = st1[r0 -- sk], ∃ fis. st1 = update(r, fis, st0) ∧ validFields(r, fis, st0)

User applied rule cut formula

And obtained the following new goals

Proof step 71:
r = r0, r0 -- sk ∈ st1, r0 -- sk ∈ st0, onlyModified(r, st0, st1), r0 ∈ st1, r0 ∈ st0, ∀ st, r1, st2. ¬ # st0 ≤ # st2 → (onlyModified(r1, st2, st) → (∃ fis. st = update(r1, fis, st2) ∧ validFields(r1, fis, st2))) ⊦ st0[r0 -- sk] = st1[r0 -- sk], ∃ fis. st1 = update(r, fis, st0) ∧ validFields(r, fis, st0)
Proof step 75:
r0 -- sk ∈ st1, r0 -- sk ∈ st0, onlyModified(r, st0, st1), r0 ∈ st1, r0 ∈ st0, ∀ st, r1, st2. ¬ # st0 ≤ # st2 → (onlyModified(r1, st2, st) → (∃ fis. st = update(r1, fis, st2) ∧ validFields(r1, fis, st2))) ⊦ r = r0, st0[r0 -- sk] = st1[r0 -- sk], ∃ fis. st1 = update(r, fis, st0) ∧ validFields(r, fis, st0)

Rule argument

[fma-arg: r = r0]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRAFMAS : (r = r0)]]