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Proof step 10 from proof prefix-trans (previous step)

st1[n] = mkblock(x1, lax1, m1), st2[n] = mkblock(x0, lax0, m0), st0[n] = mkblock(x, lax, m), n ∈ st2, n ∈ st0, dom st1 ⊆ dom st2, dom st0 ⊆ dom st1, dom st0 ⊆ dom st2, n ∈ st1 → x1 ⊑ x0 ∧ lax1 ⊑ lax0 ∧ # x1 = # lax1 ∧ # x0 = # lax0, n ∈ st1 → x ⊑ x1 ∧ lax ⊑ lax1 ∧ # x = # lax ∧ # x1 = # lax1 ⊦ x ⊑ x0 ∧ lax ⊑ lax0 ∧ # x = # lax ∧ # x0 = # lax0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ ns ⊆ ns0 ↔ (∀ n. n ∈ ns → n ∈ ns0)
Proof step 12:
st0[n] = mkblock(x, lax, m), st2[n] = mkblock(x0, lax0, m0), st1[n] = mkblock(x1, lax1, m1), n ∈ st0, n ∈ st2, dom st0 ⊆ dom st2, dom st1 ⊆ dom st2, n ∈ st1 → x ⊑ x1 ∧ lax ⊑ lax1 ∧ # x = # lax ∧ # x1 = # lax1, n ∈ st1 → x1 ⊑ x0 ∧ lax1 ⊑ lax0 ∧ # x1 = # lax1 ∧ # x0 = # lax0, ∀ n. n ∈ dom st0 → n ∈ dom st1 ⊦ x ⊑ x0 ∧ lax ⊑ lax0 ∧ # x = # lax ∧ # x0 = # lax0

Rule argument

spec: set-basic, inst: nat-set name: Subset seq: ⊦ ns ⊆ ns0 ↔ (∀ n. n ∈ ns → n ∈ ns0) subst: [ns0, ns] → [dom st1, dom st0] flags: <all paths>

Additional information

Used terms: dom st1, dom st0