Step
*
1
1
1
of Lemma
not_has-value_decidable_on_base
1. magic : ∀t:Base. ((t)↓ ∨ (¬(t)↓))@i
2. (λx.x)↓
3. ¬(⊥)↓
4. ¬(λx.x ≤ ⊥)
⊢ ¬(case magic ⊥ of inl(a) => ⊥ | inr(b) => λx.x ≤ case magic (λx.x) of inl(a) => ⊥ | inr(b) => λx.x)
BY
{ (GenConclAtAddr [1;1;1] THEN GenConclAtAddr [1;2;1] THEN SplitOrHyps THEN Reduce 0 THEN Auto)⋅ }
Latex:
Latex:
1. magic : \mforall{}t:Base. ((t)\mdownarrow{} \mvee{} (\mneg{}(t)\mdownarrow{}))@i
2. (\mlambda{}x.x)\mdownarrow{}
3. \mneg{}(\mbot{})\mdownarrow{}
4. \mneg{}(\mlambda{}x.x \mleq{} \mbot{})
\mvdash{} \mneg{}(case magic \mbot{} of inl(a) => \mbot{} | inr(b) => \mlambda{}x.x \mleq{} case magic (\mlambda{}x.x)
of inl(a) =>
\mbot{}
| inr(b) =>
\mlambda{}x.x)
By
Latex:
(GenConclAtAddr [1;1;1] THEN GenConclAtAddr [1;2;1] THEN SplitOrHyps THEN Reduce 0 THEN Auto)\mcdot{}
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