Nuprl Lemma : all-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],
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,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_implies: P ⇐ Q,
unit: Unit,
it: ⋅,
guard: {T}
Lemmas referenced :
all_wf,
unit_wf2,
it_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
independent_pairFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
sqequalRule,
lambdaEquality,
applyEquality,
hypothesisEquality,
equalityElimination,
functionEquality,
cumulativity,
universeEquality,
dependent_functionElimination
Latex:
\mforall{}P:Unit {}\mrightarrow{} \mBbbP{}. (\mforall{}x:Unit. P[x] \mLeftarrow{}{}\mRightarrow{} P[\mcdot{}])
Date html generated:
2016_05_15-PM-03_24_50
Last ObjectModification:
2015_12_27-PM-01_06_15
Theory : general
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