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Proof step 113 from proof onlymod-shift (previous step)

r0 ≠ r1, st[r -- _type] = st1[r -- _type], r1 ∈ st, r1 ∈ st1, r1 -- sk0 ∈ st, r1 -- sk0 ∈ st1, ∀ r2, sk1. r2 ≠ r → st[r2 -- sk1] = (((r2 = r1 ∧ sk1 = sk0) ⊃ st[r1 -- sk0]; st1[r2 -- sk1])), ∀ rk0. rk0 ∈ st ↔ rk0 ∈ st1, r ≠ r1 → st1[r1 -- sk0] = val ⊦ st[r0 -- sk] = st1[r0 -- sk], r0 = r, _type = sk0, r -- _length ∈ st

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 112:
st[r -- _type] = st1[r -- _type], r1 -- sk0 ∈ st1, r1 -- sk0 ∈ st, r1 ∈ st1, r1 ∈ st, r ≠ r1 → st1[r1 -- sk0] = val, ∀ rk0. rk0 ∈ st ↔ rk0 ∈ st1, ∀ r2, sk1. r2 ≠ r → st[r2 -- sk1] = (((r2 = r1 ∧ sk1 = sk0) ⊃ st[r1 -- sk0]; st1[r2 -- sk1])) ⊦ r0 = r1, _type = sk0, r0 = r, st[r0 -- sk] = st1[r0 -- sk], r -- _length ∈ st

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]