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Proof step 3 from proof log-cons-copy-new (previous step)

# kx = # ax, adr ∈ ax, kx.toSet ⊆ dom ri, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) ⊦ dups(kx), dups(ax), node-cons(fs[ax, fs[ri[kx]]][adr].key, fs[ax, fs[ri[kx]]][adr])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ adr ∈ ax ↔ (∃ ax0, ax1. ax = ax0 + (adr + ax1))
Proof step 5:
# kx = # ax, kx.toSet ⊆ dom ri, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]), ∃ ax0, ax1. ax = ax0 + (adr + ax1) ⊦ dups(ax), dups(kx), node-cons(fs[ax, fs[ri[kx]]][adr].key, fs[ax, fs[ri[kx]]][adr])

Rule argument

spec: list, inst: address-list-set name: in-def seq: ⊦ adr ∈ ax ↔ (∃ ax0, ax1. ax = ax0 + (adr + ax1)) subst: [ax, adr] → [ax, adr] flags: <all paths>

Additional information

Used terms: ax, adr