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Proof step 6 from proof range-write-in (previous step)

ri-inj(ri), key ∈ ri ⊦ adr0 ∈ ri[key, adr] ↔ adr0 = adr ∨ adr0 ≠ ri[key] ∧ adr0 ∈ ri

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ ri-inj(ri) ↔ (∀ key0, key1. key0 ∈ ri ∧ key1 ∈ ri ∧ ri[key0] = ri[key1] → key0 = key1)
Proof step 8:
key ∈ ri, ∀ key0, key1. key0 ∈ ri ∧ key1 ∈ ri ∧ ri[key0] = ri[key1] → key0 = key1 ⊦ adr0 ∈ ri[key, adr] ↔ adr0 = adr ∨ adr0 ≠ ri[key] ∧ adr0 ∈ ri

Rule argument

spec: aubifs-inv name: ri-inj seq: ⊦ ri-inj(ri) ↔ (∀ key0, key1. key0 ∈ ri ∧ key1 ∈ ri ∧ ri[key0] = ri[key1] → key0 = key1) subst: [ri] → [ri] flags: <all paths>

Additional information

Used terms: ri