Nuprl Lemma : gen_hyp_tp
∀[A:Type]. ∀[e:A]. ∀[H:A ⟶ 𝕌{j}]. ∀[z:H e].  {{{False 
⇒ True}}}
Proof
Definitions occuring in Statement : 
uall: ∀[x:A]. B[x]
, 
guard: {T}
, 
implies: P 
⇒ Q
, 
false: False
, 
true: True
, 
apply: f a
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
guard: {T}
, 
implies: P 
⇒ Q
, 
true: True
, 
all: ∀x:A. B[x]
, 
prop: ℙ
, 
exists: ∃x:A. B[x]
Lemmas referenced : 
istype-universe, 
equal_wf, 
false_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
Error :isect_memberFormation_alt, 
introduction, 
cut, 
sqequalRule, 
sqequalHypSubstitution, 
Error :lambdaEquality_alt, 
dependent_functionElimination, 
thin, 
hypothesisEquality, 
axiomEquality, 
equalityTransitivity, 
hypothesis, 
equalitySymmetry, 
Error :functionIsTypeImplies, 
Error :inhabitedIsType, 
Error :universeIsType, 
applyEquality, 
Error :isect_memberEquality_alt, 
isectElimination, 
Error :isectIsTypeImplies, 
Error :functionIsType, 
instantiate, 
extract_by_obid, 
universeEquality, 
Error :lambdaFormation_alt, 
Error :dependent_pairFormation_alt, 
Error :equalityIstype, 
productElimination, 
hyp_replacement, 
applyLambdaEquality, 
lambdaFormation, 
natural_numberEquality, 
Error :equalityIsType1, 
Error :setIsType, 
rename, 
setElimination, 
Error :dependent_set_memberEquality_alt
Latex:
\mforall{}[A:Type].  \mforall{}[e:A].  \mforall{}[H:A  {}\mrightarrow{}  \mBbbU{}\{j\}].  \mforall{}[z:H  e].    \{\{\{False  {}\mRightarrow{}  True\}\}\}
Date html generated:
2019_06_20-AM-11_17_51
Last ObjectModification:
2019_03_05-PM-00_55_09
Theory : core_2
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