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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