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[tlaplus] Proof by induction invoking the SequencesInductionTail theorem

Hello all,

I have a theorem which depends on some lemmas. One of this lemmas is the fact that "the product of two sequence products is the sequence product of their concatenation". That is:    

\A s1, s2 \in Seq(Nat) : SeqProduct[s1] * SeqProduct[s2] = SeqProduct[s1 \o s2]

SeqProduct[s \in Seq(Nat)] ==
  IF   s
= <<>>
  ELSE LET x  
== Head(s)
== Tail(s)
       IN x
* SeqProduct[xs]

For this one, im planning to reason inductively using the SequencesInductionTail theorem available on module SequenceTheorems (not saying this alone will suffice). 
Now, having the following structure:
LEMMA SomeLemma == \A s1, s2 \in Seq(Nat) : SeqProduct[s1] * SeqProduct[s2] = SeqProduct[s1 \o s2]
<1> DEFINE Prop(s) == \A s2 \in Seq(Nat) : SeqProduct[s] * SeqProduct[s2] = SeqProduct[s \o s2]
<1> SUFFICES \A s1 \in Seq(Nat) : Prop(s1) OBVIOUS  
<1>1. Prop(<<>>) PROOF OMITTED
<1>2. \A s \in Seq(Nat) : (s # << >>) /\ Prop(Tail(s)) => Prop(s) PROOF OMITTED  
<1> HIDE DEF Prop
<1>3. QED
<1>1, <1>2, SequencesInductionTail

Ignoring now <1>1 and <1>2, for the high level part i was expecting TLAPS to prove the final step <1>3 and it couldn't. 
The proof obligation generated is:
ASSUME Prop(<<>>) ,
\A s \in Seq(Nat) : s # <<>> /\ Prop(Tail(s)) => Prop(s) ,
              NEW CONSTANT P
(<<>>) ,
\A s \in Seq(S) : s # <<>> /\ P(Tail(s)) => P(s)
\A s \in Seq(S) : P(s)
\A s1 \in Seq(Nat) : Prop(s1)

which looks reasonable to me. Also tried the ASSUME ... PROVE form, but the result is the same.

Im missing something here to correctly invoke SequencesInductionTail ?


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