Nuprl Lemma : exists-unit
∀P:Unit ⟶ ℙ. (∃x:Unit. P[x] ⇐⇒ P[⋅])
Proof
Definitions occuring in Statement :
it: ⋅,
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
unit: Unit,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
exists: ∃x:A. B[x],
unit: Unit,
member: t ∈ T,
it: ⋅,
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_implies: P ⇐ Q
Lemmas referenced :
exists_wf,
unit_wf2,
it_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
independent_pairFormation,
sqequalHypSubstitution,
productElimination,
thin,
equalityElimination,
hypothesis,
cut,
lemma_by_obid,
isectElimination,
sqequalRule,
lambdaEquality,
applyEquality,
hypothesisEquality,
dependent_pairFormation,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}P:Unit {}\mrightarrow{} \mBbbP{}. (\mexists{}x:Unit. P[x] \mLeftarrow{}{}\mRightarrow{} P[\mcdot{}])
Date html generated:
2016_05_15-PM-03_24_53
Last ObjectModification:
2015_12_27-PM-01_06_18
Theory : general
Home
Index