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Proof step 172 from proof onlymod-shift (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 171:
r1 -- sk0 ∈ st1, r1 -- sk0 ∈ st, r1 ∈ st1, r1 ∈ st, ∀ rk0. rk0 ∈ st ↔ rk0 ∈ st1, ∀ r2, sk1. r2 ≠ r → st[r2 -- sk1] = (((r2 = r1 ∧ sk1 = sk0) ⊃ st[r1 -- sk0]; st1[r2 -- sk1])), r -- _type ∈ st → st[r -- _type] = (((r = r1 ∧ _type = sk0) ⊃ st[r1 -- _type]; st1[r -- _type])), r -- _length ∈ st → st[r -- _length] = (((r = r1 ∧ _length = sk0) ⊃ st[r1 -- _length]; st1[r -- _length])), sk0 = _length ∨ sk0 = _type ∨ r ≠ r1 → st1[r1 -- sk0] = val ⊦ (r0 ≠ r → (((r0 = r1 ∧ sk = sk0) ⊃ val; st[r0 -- sk])) = st1[r0 -- sk]) ∧ (r -- _type ∈ st → (((r = r1 ∧ _type = sk0) ⊃ val; st[r -- _type])) = st1[r -- _type]) ∧ (r -- _length ∈ st → (((r = r1 ∧ _length = sk0) ⊃ val; st[r -- _length])) = st1[r -- _length])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0])]]