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Step * 1 2 of Lemma make-proof-tree_wf


1. Sequent : Type
2. Rule : Type
3. effect : (Sequent × Rule) ⟶ (Sequent List?)
4. s : Sequent
5. r : Rule
6. L : proof-tree(Sequent;Rule;effect) List
7. ↑isl(effect <s, r>)
8. ||L|| = ||outl(effect <s, r>)|| ∈ ℤ
9. make-proof-tree(s;r;L)
= make-proof-tree(s;r;L)
∈ (sr:Sequent × Rule × (case effect sr of inl(subgoals) => ℕ||subgoals|| | inr(x) => Void
                       ⟶ proof-tree(Sequent;Rule;effect)))
⊢ (sr:Sequent × Rule × (case effect sr of inl(subgoals) => ℕ||subgoals|| | inr(x) => Void
                       ⟶ proof-tree(Sequent;Rule;effect))) ⊆r proof-tree(Sequent;Rule;effect)
BY
{ TACTIC:(InstLemma `proof-tree-ext` [⌜Sequent⌝;⌜Rule⌝;⌜effect⌝]⋅ THEN Auto) }

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Latex:

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Latex:

1.  Sequent  :  Type
2.  Rule  :  Type
3.  effect  :  (Sequent  \mtimes{}  Rule)  {}\mrightarrow{}  (Sequent  List?)
4.  s  :  Sequent
5.  r  :  Rule
6.  L  :  proof-tree(Sequent;Rule;effect)  List
7.  \muparrow{}isl(effect  <s,  r>)
8.  ||L||  =  ||outl(effect  <s,  r>)||
9.  make-proof-tree(s;r;L)  =  make-proof-tree(s;r;L)
\mvdash{}  (sr:Sequent  \mtimes{}  Rule  \mtimes{}  (case  effect  sr  of  inl(subgoals)  =>  \mBbbN{}||subgoals||  |  inr(x)  =>  Void
                                              {}\mrightarrow{}  proof-tree(Sequent;Rule;effect)))  \msubseteq{}r  proof-tree(Sequent;Rule;effect)


By

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Latex:
TACTIC:(InstLemma  `proof-tree-ext`  [\mkleeneopen{}Sequent\mkleeneclose{};\mkleeneopen{}Rule\mkleeneclose{};\mkleeneopen{}effect\mkleeneclose{}]\mcdot{}  THEN  Auto)

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