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Proof step 3 from proof map2 (previous step)

(a[r => o0] * R0)[rs, f, g], (a[r => o] * R)[rs, f, g] ⊦ o = o0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ (a[r => o0] * R)[rs, f, g] ↔ (a[r => o1] * R)[rs, f(r; o1), g] ∧ f(r) = o0
Proof step 5:
f(r) = o0, (a[r => o] * R)[rs, f, g], (a[r => o1] * R0)[rs, f(r; o1), g] ⊦ o = o0

Rule argument

spec: <toplevel> name: write-known seq: ⊦ (a[r => o0] * R)[rs, f, g] ↔ (a[r => o1] * R)[rs, f(r; o1), g] ∧ f(r) = o0 subst: [o1, g, f, rs, R, o0, r, a] → [o1, g, f, rs, R0, o0, r, a] flags: <all paths>

Additional information

Used terms: o1, g, f, rs, R0, o0, r, a