[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 19 from proof aux-known (previous step)

rs1 ∩ rs0 = ∅, ((r => o))(mk(rs1, f)), R[rs0, f, g], r0 ∈ rs1 → g(r0) = a0, ∀ r. r ∈ rs1 → g(r) = a0 ⊦ (r0 ∈ rs1 → (r = r0 ⊃ a1;g(r0)) = a1) ∧ R[rs0, f, g(r; a1)], (a1[r => o] * R)[rs1 ∪ rs0, f, g(r; a1)] ∧ g(r) = a0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ ((r => o))(H) ↔ H = (∅ ++ r)[r, o] ∧ r ≠ null
Proof step 21:
mk(rs1, f) = (∅ ++ r)[r, o], rs1 ∩ rs0 = ∅, R[rs0, f, g], r0 ∈ rs1 → g(r0) = a0, ∀ r. r ∈ rs1 → g(r) = a0 ⊦ r = null, (a1[r => o] * R)[rs1 ∪ rs0, f, g(r; a1)] ∧ g(r) = a0, (r0 ∈ rs1 → (r = r0 ⊃ a1;g(r0)) = a1) ∧ R[rs0, f, g(r; a1)]

Rule argument

spec: maplet name: maplet seq: ⊦ ((r => o))(H) ↔ H = (∅ ++ r)[r, o] ∧ r ≠ null subst: [H, o, r] → [mk(rs1, f), o, r] flags: <all paths>

Additional information

Used terms: mk(rs1, f), o, r